Goals from Marcus Rashford and Anthony Martial saw United past Crystal Palace 2-0 on Thursday as they continued their top-four push in the Premier League.
United have a short turnaround ahead of playing Chelsea and Solskjaer had questioned why Frank Lampard’s team were afforded 48 hours more rest.
But the United manager said his players were ready to go for the clash at Wembley.
“Of course, anyone can hold their hands up at any moment and say, ‘I want to sit out this one’.
“We’ve got players on the bench desperate to join in, but it was forced with Brandon [Williams] and Luke [Shaw] not being available today.
“Timothy [Fosu-Mensah] did great and Scott [McTominay] has been fantastic. He took a shift for Nemanja [Matic].
“We’ve got the players who’ve had the chance over this period to take players off, being three goals up in many games after 60 minutes. We’ve been fortunate in that respect.”
United are fifth in the Premier League table, a point behind Chelsea and level on points with fourth-placed Leicester City with two games remaining.
The Red Devils boss believes his side earned the right to smile after claiming a crucial three points against Palace.
“It is a tight game and didn’t get the rhythm in our passing but two fantastic goals won it for us,” he told BBC Sport.
“Marcus Rashford and Anthony Martial are enjoying themselves, when they go out onto the pitch for a shift, they go out with a smile and they defend each other too.
“We need to smile and go into this, we have earned this right, no-one thought in January that we would be in with a shout for top four. We have done fantastic since the restart.
“These are the games that matter. That is the thing at Manchester United, you have to step up and show your personality.”