Chelsea were held by Liverpool to 2-2 draw after 120minutes but it was the Reds that smiled away with the trophy after the game was decided by penalties.
Most pundits and fans did not give Chelsea any chance in the game following their shambolic defeat against Manchester United in the league last season.
Olivier Giroud had put the side in the lead in the first half before Liverpool Sadio Mane equalised and they ended up playing extra time.
Tammy Abraham became the villain for Chelsea after his penalty was saved by Liverpool new boy Adrian.
Liverpool take on Southampton over the weekend and Klopp is ruing the fixtures.
“Actually we don’t have time for that!” he joked when asked if his players will now be able to touch the famous ‘This is Anfield’ sign.
“We play on Saturday again, we have to find a way to be ready for that game.
“After 90 minutes, I think, when it was close to the final whistle, Frank Lampard asked me: ‘Where do you play and when do you play [at the weekend]?’ And I said ‘Southampton on Saturday – congratulations!’
“Nobody wanted extra-time tonight, they play Leicester at home on Sunday but they played last Sunday so there was no advantage tonight but for the next game for both it will be pretty tough.
“But we have to be ready again and that’s my present to the players to help them recover so that they are ready for the game.
“It was a big fight tonight and I didn’t know before the game how good it would be when you win it, but it’s brilliant, it’s really big.