Pep Guardiola welcomed the win but felt his Manchester City side were still far from their best after beating West Ham 4-1 on Saturday.
Erling Haaland struck twice as the champions rediscovered their goalscoring touch at the Etihad Stadium to secure back-to-back Premier League victories for the first time since October.
The result took more heat off City after they claimed only their second win in 14 games in all competitions at Leicester last week, but Guardiola does not feel his team are back to their old selves yet.
The City manager said: "We saw in many years our level and we are not at our level. We won, I am so happy and it helps us.
"But you judge results, (when) our performance was not good.
"I’m so happy for the guys, and the work ethic, but in the first minutes deserved to be 0-1, 0-2 and we were lucky with the first goal.
"We are a strong team (when) we run a lot and have the composure, but now we don’t have it.
"I’m very pleased for the result but you cannot ask me if the old City is back. If you saw the game, we are not.
"You saw many times during the years what we have done with the opponents."
West Ham spurned two gilt-edged chances to take the lead before City went ahead when Vladimir Coufal turned Savinho’s cross into his own net.
Phil Foden got on the scoresheet for the hosts too but their best player was in-form winger Savinho, who also set up both of Haaland’s goals.
Guardiola said: "Has a lot to improve – he’s not aggressive enough without the ball, he’s a little bit soft in many departments, but right now has something special and brilliant that helps the team a lot.
"He ‘scored’ a goal, was a bit lucky, but the two assists were brilliant. I’m so happy for him and he deserves to play."
West Ham’s defeat, coming after a 5-0 thrashing at Liverpool, did nothing to ease the pressure on manager Julen Lopetegui, especially with his predecessor David Moyes spotted in the crowd.
The former Real Madrid and Spain boss could, however, bemoan his luck after early missed chances by Mohammed Kudus and Tomas Soucek, while Crysencio Summerville was harshly penalised for a foul when clean through.
Lopetegui, whose side did manage a consolation through Niclas Fullkrug, said: "It is not easy to explain the match. We deserved more in my opinion. A lot of little details worked against us.
"Not only did we not take advantage of two clear situations – we have to do better – but after they scored one goal we were very unlucky.
"We had a very clear situation with Summerville on (Manuel) Akanji. It was not a foul but the referee said foul. It was an unfair situation.
"We did very good things and positive things, but in the end it was not enough."
Elsewhere, Chelsea boss Enzo Maresca blamed a lack of clinical finishing after Jean-Philippe Mateta's late equaliser salvaged a 1-1 draw for Crystal Palace at Selhurst Park.
Cole Palmer opened the scoring in the 14th minute of a first half dominated by Maresca’s visiting Blues, who squandered a number of chances to pad their lead before the Frenchman levelled eight minutes from time.
Fourth-placed Chelsea, once touted as title contenders, are now winless in their last four Premier League meetings and have just one point more than Newcastle, who edged closer to the Champions League places with victory over Tottenham.
Maresca said: "Two weeks ago, three weeks ago, we were talking about the title race. We knew that Newcastle, Aston Villa will be there, City will be, for sure there.
"So it’s for me, it’s not about the table. It’s just about seeing how we can improve things.
"Today, the performance for me was very good on the ball, off the ball.
"But this moment of the season, I knew that is going to happen in any season for any team, that you have some moment that you are not able to win games.
"The reason why? I think every game is different. Sometimes it’s for one reason, sometimes it’s for different reasons.
"But today, if I have to decide the reason why we didn’t win the game, I think it’s just try to be clinical when you have the chance to kill the game.
"If you continue to be open, open, open at the end, you’re going to concede."
Jadon Sancho was the spark behind Chelsea’s opener, outsmarting Chris Richards before darting down the left, cutting in and slipping to Palmer, who scored his 13th of the Premier League campaign.
The opener stood as the game’s only goal until the 82nd minute, when Mateta was set up by the unselfish Eberechi Eze.
Maresca made six changes from Chelsea’s Ipswich defeat, including a full Premier League debut for the impressive 18-year-old Josh Acheampong, who he hailed after the stalemate.
"All of the players for me were good today, but if I had to decide for one, I think Josh was our best player," he said, explaining, "because of the age, because it was the first game.
"Josh for me can be a top player for this club, but he needs the right path, the right moment. With young players, you have to decide which moment, and we decided today because he was ready today.
"I think he showed how good he is, and now again, because of the age, he has to slow down, work hard and take the next chance."
Palace have now moved four points clear of 16th place Everton below them, though the Toffees have a game in hand.
After hovering around the relegation zone – occasionally dropping in – in 2024, they have moved within one point of Manchester United in 14th, and sit just three points behind 12th-placed Spurs.
Eagles boss Oliver Glasner agreed his side probably showed Chelsea too much respect early on, but was pleased by their determination to reverse their fortunes after the break.
"I think at the end it’s a deserved point," he said.
"With all (Chelsea’s) quality, it is just not possible to defend every situation and with every chance they’re creating with every ball you lose, the confidence goes down.
"That’s normal, but really, really, I’m really pleased with this, with the character not to lose your belief stay in the game, and knowing that we can come back.
"And this is what we were saying at half-time, one two adjustments, and those are stay guys, we are in the game.
"But this is also a progress we have. We have to show that we can play in the same way we played, let’s say, the last 60 minutes, over the whole period, and then it’s possible to win against a team like Chelsea."
