United dominated the first-half at Molineux and deservedly took the lead through Anthony Martial.
But the visitors were punished for not doubling their lead as Ruben Neves scored a stunning goal to equalise after 55 minutes.
However, Rui Patricio pulled off a great save to deny the World Cup winner and ultimately win a point for his side.
Speaking after the game, Solskjaer was positive about his side's performance.
He said: "We dominated possession, we get the first goal and second half we know they'll come out like a house on fire.
"They probably got the goal they deserve. I thought we took control again and could have won it.
"First half was a mature performance. Second half was a bit sloppy. We are improving. We are a young team who will learn, we learned on the pitch today.
On the penalty, Solskjaer added: "We get a penalty that normally would get us another two points, sometimes the keeper makes a good save."