Oxlade-Chamberlain scored twice on his return to European action, including a truly superb outside-of-the-boot effort from range to put Liverpool 2-0 up.
Sadio Mane and Mohamed Salah also found the net, though Klopp didn’t think his side were anywhere near their best - but he was more than happy with their goalscoring form.
“It was a pretty stiff first half," Klopp said. "Then we could show the boys a couple of spaces which they could and should use in the second half. Then we scored the second goal - by the way, the first goal was very brilliant and the second goal even nicer, and all our goals were unbelievably beautiful.
“It was absolutely a great moment for him, but I would say with Ox his performance was exactly the same as the performance of the team – the goals were great but all the rest could have been better."
Liverpool stayed within a point of group leaders Napoli with the win, but the German wasn't happy with his side's overall performance on the night.
With Tottenham winning 5-0 on Tuesday, Klopp thinks his side will have to improve ahead of their Premier League clash on Sunday.
"There were good moments,” he told BT Sport . "The start was brilliant, we were kind of fluent and asked them a lot of questions but then we started - I'm not sure why - to lose patience and some easy balls.
"But all four goals were brilliant and we had chances to score more. Job done. In the years before we would have drawn it, maybe even lost, but all's ok.
“It was intense, we needed concentration. Our opponent brought in their tallest player and they did well from the first and second balls. So I didn't enjoy the game too much, but I enjoyed the result."
"We've just had two away games that were both difficult for different reasons. I don't know where we are now but I know where we need to be on Sunday.
"It's a refreshed Tottenham. Of course, the second they meet us they're back on track! But we're a different team to Red Star Belgrade, just like Tottenham are different to Genk."
Reds captain James Milner, meanwhile, hailed Oxlade-Chamberlain’s hard work off the pitch as he finally reaps the rewards of an arduous return to fitness.
"Everyone's delighted for him,” Milner said. “It's the things that people don't see behind the scenes, the hard work around the training ground.
"He's got a great strike and he's good in those pockets. It's great to have him back and he's another option in that midfield, where there's already great competition for places."