United travel to Aston Villa on Sunday before Leicester visit Old Trafford on Tuesday. The rearranged fixture with Liverpool, postponed on Sunday following fan protests, has been scheduled for 48 hours later on Thursday.
"It's unheard of," said Solskjaer. "It's made by people who've never played football at this level. Physically, impossible for the players to do it after being here, doing Sunday-Tuesday, Thursday, it's impossible. So we've not been dealt a good hand but we'll have to play as well as we can.
"We're going to need everyone in these four games. We'll have to see how we are on Sunday morning. We play two o'clock on Sunday. It's a short turnaround but we'll have to be ready."
United lost 3-2 on the night against Roma but set up a final with Villarreal in Gdansk after taking a commanding 6-2 lead from the first leg. Edinson Cavani scored twice to add to his two goals at Old Trafford while David De Gea had to be in top form, making 12 saves.
"David was vital, man of the match, stand out," said Solskjaer. "The final is still three weeks away and there are many games but he's put in performance. You've got to perform and you keep your place in the team when you play well.
"When you are in a final you've a chance. I'm so happy for the boys that they've got something to look forward to."