Rashford struck in victory at Brighton on Saturday.
Solskjaer said, "I'm very happy for Marcus to get that goal. He was just a couple of inches offside on a counter-attack we had, with a great cross from Mason [Greenwood].
"We did see some moments that we didn't see last week.
"We're getting a little bit better but I think we need to admit sometimes you get away with one, and today we probably didn't deserve more than one point."