The win secured Dortmund top spot in their group and qualification for the knockout stage with a game to spare, leaving Ajax fighting with Manchester City for a place in the Europa League and Real Madrid taking second place in the group, but Klopp said it was hard work in Amsterdam.
"It was no walk in the park," he said.
"I think everybody saw that.
"Ajax had lots of possession in the first half and we kept our discipline while turning defence into attack for us was sensational."
Marco Reus, Mario Gotze and Robert Lewandowski (two) got the goals for the defending German champions, who after failing to come through the group stage of the Europa League two seasons ago and the Champions League last year, finally appear to have found their feet in Europe.
"If they continue to play like this, then they don't need to care about who they are drawn against in the knockout stage," former Bayern Munich player, coach and president Franz Beckenbauer told Sky television.
"Anybody who can beat Real Madrid so easily can certainly harbour hopes of winning the Champions League.
"I'd like to see Bayern against Dortmund in the final."