Bournemouth manager Eddie Howe tells BBC Sport: "We thought we had hung on for a point, we had chances to win it too, I am disappointing for the players and the supports.
"The second half was bitty, we wanted that to be the case. I am more disappointed for the foul given against Lys Mousset, but these things happen. I am enthused by the performance, which was better than our first two.
"We started really well, very positively. Jermain had a chance to make it 2-0, we created more chances today than in our first two games, but we need to start getting some points quickly.
"You cannot prepare this game to dominate the ball. We know it would be a different test, we had to be disciplined which I felt we were, but one or two moments of class from them can hurt you."
Manchester City manager Pep Guardiola to BBC Sport: "Winning the last minute is always special. It was a tough game, it is always complicated against Bournemouth. They play long balls, balls into the channels and play set-pieces but we got into the game. We tried, our finishing was not good but we are there.
"Frustrating for us? Why? We were better against Tottenham last season, had 60% possession but did not score.
On Raheem Sterling red card: "I do not understand the decision. Hopefully they can call me and explain why. I can speak after winning. I am talking about the decision, I am not the referee. It is what it is.
"We gave them the ball back but the defender did not move."
Louis Porter: I have no idea what is going on...
Parm: That's is a joke. Getting a second yellow for over celebrating. The refs just don't understand the emotions of football.
Dave: Mike Dean making up rules again
Bournemouth defender Charlie Daniels tells BBC Sport: "There was only five minutes of added on time so ask the referee why we played seven. Then in the lead-up to the goal, he awarded a free-kick which was perfectly a timed tackle by Lys Mousset. It was gutting for us to concede after that and I would like to found out where he got that extra time from.
"It was a nice goal (by me). I thought why not have a crack at it and fortunately it went in."
Former Spurs striker on Final Score
There was so much about this game that is getting my knickers in a twist.
The biggest controversy for me is the sending off.Copyright: AFP
Raheem Sterling scores a goal in the dying minutes, he is euphoric and goes to celebrate with the fans and receives a red card for it.
Who is Mike Dean appealing to by sending him off for that? It's certainly not the crowd.
Manchester City midfielder Bernardo Silva tells Sky Sports: "It was a tough match for us. We did not start well but we played well after that/ All the games are difficult, all the team are competitive but we got the three points.
"The manage asked me to be myself, as I did last season for Monaco. I need to get adapted to the team and I am feeling well."
Manchester City defender Vincent Kompany tells Sky Sports: "Madness. The first thing I did was say to Benjamin Mendy and Bernardo Silva, 'welcome to the Premier League'. I thought we played well, like we did against Everton. We did not score our chances but we have big, fast, strong players and anything can happen. We deserved to win, but they made it hard for us.
"Our strength of character showed and we dealt with the physical challenge well. Overall, we won 95% of our challenges, which is a good sign.
On Charlie Daniels goal: "It was an unbelievable goal, from an angle I did not think was possible. No matter how much you dominate, anything can happen."
On Raheem Sterling red card: "I do not know whether the crowd ran to Raheem or he ran that way. It was too many emotions to control."Copyright: Reuters
All eyes on referee Mike Dean at the final whistle. We have said that before, haven't we?
Was time up? What was the point in sending Raheem Sterling off after celebrating?
Stay with us for full reaction.
- Copyright: Getty Images
Bournemouth players surround the referee Mike Dean as he blows for full-time.
A dramatic ending to this game.
Raheem Sterling given a second yellow card, which means a red and is sent off by referee Mike Dean for celebrating with the away supporters.
I make that 10 minutes into added time.
- Copyright: BBC
Pandemonium in the away stand.
City do not give up and get their winner late on.
Kevin de Bruyne to Raheem Sterling in the area.
Sterling pops it wide to Danilo, who gives it back to Sterling to finish into the far corner.
The shot takes a nick off Andrew Surman's heels, which gave Asmir Begovic no chance.
Sterling and the City players run to celebrate with the away supporters and the police get involved to try and restore order.Copyright: Getty Images
At the other end, Joshua King forces Ederson into a low save to his right.
A good stop.
Kevin de Bruyne puts in the corner...
...which Bournemouth goalkeeper Asmir Begovic comes off line to punch away.
- Copyright: Getty Images
More defending for Bournemouth to do late on.
Charlie Daniels heads Leroy Sane's cross away for a corner...
Copy and paste: Yellow card.
Bournemouth's Adam Smith now.
Sub being subbed.
Benik Afobe cannot continue after taking a knock when challenging for the ball with Vincent Kompany.
Lys Mousset takes his place.
That will add some more seconds on.