Solskjaer fielded a second-string line-up for Tuesday's 2-1 home loss to Leicester City, which comes only two days after they won 3-1 away to Aston Villa in the Premier League.
The Red Devils' fixture pile-up has been compounded by their run to the Europa League final, having completed their passage on Thursday with an 8-5 aggregate win over Roma.
But United's backlog was made worse by their postponed league fixture against Liverpool due to fan protests at Old Trafford.
United play that fixture against Liverpool on Thursday before another league match against Fulham on Tuesday.
Solskjaer acknowledged the situation the postponed Liverpool fixture had created but called for fairer re-scheduling.
"It can’t be like this again," Solskjaer said post-game. "You can’t play Thursday, Sunday, Tuesday, Thursday - it is impossible.