City's 1-0 win at Bournemouth on Saturday moved them back top, with Liverpool unable to reclaim that spot a day later as they drew 0-0 at Everton in the Merseyside derby.
Klopp's side have failed to score in three of their past four matches in all competitions and they also drew 0-0 in their last away Premier League game, at Manchester United.
But although the Reds have ceded pole position to City as they hunt a first title of the Premier League era, Klopp believes further twists could come over the last nine games.
"We are positive – how couldn't we be positive?" Klopp said to Liverpool's official club website after the stalemate at Goodison Park.
"There is a lot to come and a lot of games to play. What brought us here was the stability the boys showed.
"We are difficult to beat, which is very important in football. And we created, still, in difficult games, which is very important in football.
"Then you have to finish them off, which we did very often but not [at Everton].
"The dynamic [at the top of the Premier League] changed a little bit – now we are second, they are first.
"The season is not over and we will not give up."
He has said: “Of course, we’re only a point behind City.
“There’s still only a game twist if they drop points, so we’re there to capitalise on that [and] that’s what we’ve got to do. They’ve been good at closing the gap on us and have taken over from us. They’ve been good at piling on the pressure, but now we do that to them and hopefully they feel it because we will push them the whole way.
“We’ll push right to the final whistle and kick against Wolves in the last game of the season. If we fall short, we fall short, if we don’t then great.
“But we’ll fight for everything now and we’ll push them the whole way. If they drop points then we need to be in a position to capitalise on that like they’ve done to us.”