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.