Liverpool went to north London without winger Mohamed Salah, who was with the Egypt squad for the Africa Cup of Nations, and without combative midfielder Wataru Endo, who joined up with Japan for the Asian Cup.
Their defensive talisman and captain, Virgil van Dijk, was also out through illness.
Dominik Szoboszlai, Andrew Robertson, Kostas Tsimikas, Thiago Alcantara, Stefan Bajcetic and Joel Matip are among those injured at Merseyside.
"That's a really good football team we missed. Football is like that. Sometimes you have them all available, it's pretty rare, and sometimes you don't have them available. I'm super-happy," Klopp told reporters.
"First half you could see it didn't click. It was not because of new players or whatever, it was just the timing was bad and that doesn't help.
"I said to the boys in the meeting before the game: humans are like that. It's a tough game, nobody comes to Arsenal and wins just like this (clicks fingers)."
Having already booked their place in the League Cup semi-finals and Europa League round of 16, the Premier League leaders knocked Arsenal out of the FA Cup thanks to an own goal by Jakub Kiwior and Luis Diaz's fine finish in injury time.
"The boys enjoyed the game, at least in the second half. Staying in a game that looked in the first half like that, then growing into a game, is a pretty special thing to do. Especially an away game," the German said.
Liverpool next host Fulham in the first leg of the League Cup semi-final at Anfield on Wednesday.
