"That must be what we do against Liverpool - make them play how they don't like".
Klopp's side had plenty of chances to get on the scoreboard, Sadio Mane firing wide in first-half stoppage time and Mohamed Salah seeing his free-kick tipped over magnificently by the impressive Lukasz Fabianski.
It was Liverpool's first defeat since October, but the points were priceless for Swansea, who cut the gap between themselves and those above the relegation places to just three points.
The 25-year-old midfielder was the key man for Swans upfront as they secured all three points at the Liberty Stadium but Ayew could only last for 79 minutes as he was replaced by veteran striker Wilfried Bony.
"It was only one moment when I had enough, it wasn't to do with the fact we were 1-0 down".
"We didn't keep the positions we wanted to be in".
"But because of the first-half we weren't that secure or confident in what we were doing". "We wanted to do it differently, but it didn't work out", the German told Sky Sports.
Liverpool piled on the pressure in the closing stages but Can and Salah wasted stoppage-time opportunities before Firmino nearly broke Swansea hearts.
Swansea remain bottom of the league - on goal difference from West Brom - but it is now only one defeat in six games under new manager Carlos Carvalhal.
Van Dijk made a hash of Clucas' corner and his attempted clearance struck Federico Fernandez to fall perfectly for Mawson, who swept home. Sorry, I reacted one time, I remind myself I am a human being and not a professional manager who takes that all the time and they can say whatever they want. I have no problem with that. Swansea knows to win this game today they needed our help and unfortunately we helped them.
"We could have equalised at the end, but didn't have that luck".
"I am more frustrated about the performance than the result", said Liverpool boss Jurgen Klopp.
"They are like a Formula One vehicle". "But at 4pm in London it will be hard to speed, they would be a auto like any other".