The Reds said a "severe outbreak" at the club meant they could not field a team against the Gunners.
However, Klopp says defender Trent Alexander-Arnold is the only player to actually test positive.
Anyone with a false positive result was still unavailable for Sunday's FA Cup third-round tie against Shrewsbury.
Klopp named four teenagers in his starting line-up with one of those - Kaide Gordon - scoring the equaliser as the Merseyside club came from behind to win 4-1.
"This was the team we could line up with today and the boys did really well," said the Reds boss.
"We had last week a proper outbreak and it showed up that we had a lot of false positives but the rules are like they are so all these players who are false positives couldn't play.
"The only real positive came from Trent Alexander-Arnold and all the rest were false positives."
The Reds temporarily closed their first-team training centre on Wednesday after assistant manager Pep Lijnders became the latest to have to isolate.
Lijnders had taken charge of last weekend's Premier League draw at Chelsea, with Klopp already isolating after a suspected positive test - although the German was able to return to the bench against Shrewsbury.
Their Carabao Cup semi-final first leg will now be at Anfield on Thursday and the second at Emirates Stadium on 20 January, both at 19:45 GMT.