Rashford put United in front in the first half -- his first goal from open play since August -- before Adam Lallana's late equaliser and Solskjaer was so impressed with the 21-year-old's display the Norwegian said it was his best game since he took over from Jose Mourinho nearly a year ago.
"It was his best game, maybe, in 10 months for me," said Solskjaer. "He runs off the shoulder, chases, defends well and got hold of the ball. You could see he is growing and getting stronger.
"I'm disappointed we can't sit here and talk about a win but of course the performance is very positive.
"They're so disappointed in the dressing room but we played against a very good team and we'll kick on."
Solskjaer takes his team to Partizan Belgrade in the Europa League on Thursday before a trip to Norwich on Sunday.
"I don't know how [Tuanzebe] is but hopefully both him and Jesse will be back soon," said Solskjaer.
"Anthony [Martial] will be able to play more. There is a test on Paul to see where he's at and when he'll be back. Luke, not too long. [Nemanja] Matic has played on with a little problem."