Klopp said: “We don’t waste energy thinking hopefully they (Man City) lose.
“Now we have to really recover and to play the FA Cup final because there is no mercy. The situation, qualifying for the finals, is massive.
“Their quality and mentality and character is the reason why we are where we are. I’m not surprised they can do something like this but I don’t take it for granted.
“We had an outstanding and incredible mentality. We needed time to find our way into the game and our opponent was there in the beginning, really aggressive.
“In the last 10 or 15 minutes we really stated controlling the game, it was the way we had to do it. We scored a second, incredible, goal.
“Luis (Diaz) was sensational and Sadio made the world of it. Then we had to dig deep, they had moments and a big chance with (Danny) Ings.”
But the hosts’ lead lasted just three minutes during a crazy opening and Matip stabbed in after Tyrone Mings failed to deal with Trent Alexander-Arnold’s free-kick.
“I don’t know, he felt a muscle. He is quite positive but I’m not sure what I can make of that,” he added.
Liverpool knew they needed to find a winner and Alexander-Arnold’s free-kick whistled wide before Kostas Tsimikas’ brilliant covering tackle denied Watkins after the break.
But the goal they craved came with 25 minutes left when Luis Diaz was allowed to cross from the left and Mane glanced in.
The visitors still had to survive a late Villa push and, after Alisson denied Ings, the striker saw a goal correctly disallowed for offside.
“We have got to take those big moments we created and we’re slightly frustrated we didn’t score more than once,” said Villa boss Steven Gerrard.
“We were ambitious, brave, courageous and went toe-to-toe with one of the best teams in the world. It was a massive challenge and a big ask but I’m extremely proud of what they brought. We knew we would have to suffer at times against this team.
“We’re disappointed with both goals we conceded and frustrated we couldn’t keep the lead for longer. I can’t ask for any more from the players. We made Liverpool work extremely hard.”
Gerrard also revealed his frustration at referee Jon Moss’ performance after the official angered both sides at Villa Park.
“I hope the referee’s performance is looked at,” he added.