The German goalkeeper spilled Oliver Norburn's free-kick in the 72nd minute, and Jonny Smith pounced to net Tranmere's opener.
It was a bad mistake and reminded those in attendance of the errors he made in the UEFA Champions League final defeat to Real Madrid back in May, but Klopp pointed out a mix-up between Pedro Chirivella and James Milner also led to Tranmere's second goal from Amadou Soukouna, per LiverpoolFC.com:
"Nobody likes that goal, but if we talk about the second goal—I think it was Millie's fault together with Chirivella. Two brilliant footballers make this mistake, which one was bigger? I would say the mistake of the two boys, but we don't talk about it.
"Loris concedes that goal, but we cannot start a story always after each mistake. Mistakes will happen; I don't like it, he doesn't like it, but it will happen, so let's carry on and make the best of all these situations by learning from them. That's how it is."
Klopp added that the free-kick from Norburn was "an ugly shot" and "not easy to deal with," per the Liverpool Echo:
Per the Mirror's David Maddock, Karius is reportedly set to remain as Liverpool's No. 1 in the 2018-19 campaign despite it being widely expected he would be replaced following his disastrous performance against Real.
In the 3-1 defeat to Los Blancos in Kiev, the 25-year-old was at fault for allowing Karim Benzema to intercept his throw to score the opener and then let a speculative Gareth Bale effort through his fingers for Madrid's third.
Liverpool fans are sure to be concerned that if Karius looked nervous in a meaningless friendly against a League Two side on Tuesday, he will be severely tested and potentially make more costly errors when the Premier League begins again in August.
The first half against Rovers had been largely positive for Liverpool as Rafael Camacho, Sheyi Ojo and captain Adam Lallana put them 3-0 ahead at Prenton Park.
Klopp then made 11 changes at the break before a half to forget as Tranmere got themselves back into the game.
Karius' blunder will be the main concern from the second half, and future Liverpool opponents will likely be relishing the opportunity to test a goalkeeper low on confidence.