The Black Cats pushed Manuel Pellegrini's men all the way at the Stadium of Light on Tuesday evening, but eventually succumbed to Sergio Aguero's eighth goal in as many games as they lost 1-0.
That left them rooted in the bottom three, four points adrift of safety with just 14 games remaining.
However, January signing Kirchhoff is certain they will dig themselves out of trouble if they continue to perform as they did against City, with matches against Liverpool, Manchester United and West Ham to come.
He said: "We have had a hard season trying to stay in the league, but this evening we saw what we are able to do when we put this much intensity into a game.
"We were capable of getting a point or maybe a victory against City, one of the best teams in the league
If we put that intensity into every game, we will be able to stay in the league, we will have no trouble winning against teams at the bottom.
"We have to go on, we have to work hard, we have to play hard, we have to stay on the pitch as a team, as a good squad and then we will be successful."
Aguero's 16th-minute strike ultimately decided the game, but had it not been for City goalkeeper Joe Hart, who denied Jermain Defoe, Billy Jones and debutant Wahbi Khazri, things might have been very different.
Manager Sam Allardyce was hugely disappointed by the result, but delighted with the performance of his new-look team, and no more so than with Kirchhoff, whose display in central midfield he described as "one of the top performances of any midfielder for any team" this season.
The 25-year-old's German's evening was in sharp contrast to his debut as a substitute at Tottenham on January 16, when he was thrown on as a central defender and deflected a shot past keeper Jordan Pickford before conceding a penalty.
Kirchhoff said: "That's football
I have been playing now for almost eight years and you get evenings when everything goes wrong and you get evenings when everything goes right.
"You have to get on with it and do your work, play your game, stay confident, try to do your best every day and when you are on the pitch, try to get your performance on it
That's what I do.
"When I have a bad game, it doesn't kill me and I don't think about it for more than one night
You have to struggle on, you have to work hard and be fit for the next game, and tonight I showed what is my strength and what I can give to the team.
"I am sure that there will be evenings when I am not in this condition and I will not play as well as tonight, but that's life
Just stay calm and be relaxed, try to give your best and help the team to win games."
Source : PA
Source: PA