The Reds won 2-1 thanks to a stoppage-time winner from goalkeeper Alisson.
Allardyce was furious after the game about a disallowed goal, as well as referee Mike Dean's involvement in Liverpool's equaliser.
But Klopp had no problem with how his side won the game, claiming only one team was playing football on the day.
"I didn't think for a second that anything went in our direction," Klopp said.
"I saw one team playing football all the time and one team getting all the free-kicks, so when we get one free-kick today, if it is not right, I am absolutely fine with that."