Lukaku was handed a start for the Cup triumph.
Solskjaer said, "He is improving. He has had his time off over Christmas and now he is getting his fitness back. He needed the 90 minutes, but I thought he took the ball well with a great pass from Alexis – that's two in two for him now he has made which is also a positive."
The manager also played down an injury concern for Alexis Sanchez.
"He was feeling his hamstring towards the end and he should have told me a minute before because I had just made two subs and I didn't have to take one off in the end. I think he will be OK, but he was tired and hopefully it is not a bad reaction so we will see once we get closer to next week."