With United's game against Liverpool rearranged after the initial fixture was postponed due to fan protests at Old Trafford, the Red Devils were left facing a run of three Premier League matches in five days.
United won the first of those on Sunday at Aston Villa, but Solskjaer made 10 changes as Leicester came to Old Trafford on Tuesday - and the Foxes left with three valuable points to boost their top four hopes.
Solskjaer will likely revert to a full-strength XI for the visit of Liverpool on Thursday, where a defeat for Klopp's men would all but end their Champions League qualification hopes.
Klopp is no stranger to fixture congestion; the club famously had to play two matches in successive days on different continents last season due to their involvement in the Carabao Cup and FIFA Club World Cup, and blasted the scheduling of three United matches in five days as "a crime".
"Not exactly what I expected but I knew he had to make these changes," said Klopp.
"I said it 500 times that with all the things that happened, and the protests at Manchester, to play Sunday-Tuesday-Thursday is a crime. It is.
"But it is not the fault of Ole Gunnar Solskjaer and the players. My question to myself was: 'Would I have done the same?' Yes. You have to. You have to.
"We are late in the season, all the players played a lot of games. United went to the Europa League final so that means an awful lot of games and now you get Sunday-Tuesday-Thursday. That is not possible.
"But the weekend after is a weekend off for United. I am not the guy who is doing the schedule and fixture list but when we thought about how it could work out there was no Tuesday and Thursday game and we would all have played all the games.
"You could have moved one West Brom game (who Liverpool are due to play on Sunday) but that didn't happen.
"The explanation from the Premier League was that no other team should suffer because of the things (protests) that happened in Manchester. Let me say it like this - that didn't work out pretty well.
"A little bit West Ham, a little bit Liverpool (suffered). But if we don't qualify for the Champions League it is not the fault of Ole Gunnar Solskjaer and his team selection or the Premier League, it is our fault.
"But in this specific case I think things could have been done differently definitely but we get more and more used to things that rarely go in your favour or direction."
Additional reporting by PA.