Liverpool beat Wolves 2-0 at Anfield on Sunday thanks to two goals from Sadio Mane but City came from behind to win 4-1 at Brighton to keep their noses in front.
It meant Liverpool ended the season on 97 points, the third-highest tally in Premier League history, but fell agonisingly short of winning their first English top-flight title since 1990.
“People might say we could have done this or that but not really, I don’t think (we could have done any more),” Liverpool manager Klopp told Sky Sports.
“City were lucky in moments, we were lucky in moments. It was about staying in the race and believing and that’s what we did.
“When your opponent is City, it’s difficult. They couldn’t get rid of us and we couldn’t get rid of them. Being second in the Premier League is not what I wanted but we have to see it as the first step for this team.”
This season, however, could yet see Liverpool win European club football’s most prestigious trophy if they beat English rivals Tottenham Hotspur in the Champions League final in Madrid on June 1.
And Klopp said: “We have three weeks to prepare for the Champions League final — let’s give it a go.”
Would you like to place a soccer bet? Click here to get started in 3 easy steps.