The victory took City back within six points of Arsenal at the top of the Premier League with 13 games remaining.

City captain Silva told Sky Sports: "For the distance that we have to Arsenal, coming here - it is the toughest place in the Premier League by far - but we needed to go for another goal.

"When I scored, I was happy but we needed another and Erling got it.

"I feel the whole team knew before the game if we lost it then the title race was probably over. We felt like we needed to win.

"The hope is there and we are going to fight until the end. We need to keep doing our job that we haven't lately."

It was only City's second win in seven games and manager Pep Guardiola was not getting carried away.

Guardiola said: "Six points is better than nine, but it's still a lot considering how strong Arsenal are in all departments.

"But 13 games is a lot in the Premier League. The FA Cup is coming, the final of the Carabao Cup, the Champions League is here. There are many games, injuries, every team playing for something.

"The last 10 games, from my experience, are not a drama but so difficult. The important thing is to be there and improve."

The game ended in controversy as Rayan Cherki scored what would have been a third City goal from inside his own half but play was pulled back for a foul on Haaland by Dominik Szoboszlai.

Szoboszlai, who had scored Liverpool's goal with a stunning free-kick after 74 minutes, was sent off.

Guardiola said: "Common sense, come on. I know he pulled him but how many pulls are there in a game when referees play on?

"Give a goal, 3-1, Szoboszlai can play and we're happy."

Liverpool head coach Arne Slot was angered and disappointed by the result.

Added-time goals have cost his side eight points this season, and had that not been the case they would be comfortably third instead of sixth and five points behind fourth-placed Manchester United.

"I am feeling anger and disappointment because, first half, City were the better team without creating that many big chances except the one from Haaland, but the improvement we have made since three or four months ago was visible for everyone," he said.

"It was a fantastic second half and I was expecting to be more than 1-0 up and then we conceded two goals.

"Second half, our standards went up, we were pressing them all over the place and that is the biggest improvement we have made, the whole team is now able to compete against one of the best teams in England.

"If you compare that to three or four months ago, you see so much improvement but the issue is you don't see the improvement in the league table. That is always the most important reflection of where you are."