The Red Devils had to work hard for the three points, and were fortuitous that one of the visitors' goals was disallowed for a very close offside due to VAR.
But Solskjaer was pleased at the spirit and attacking inventiveness of his team.
He told BBC Sport post-match: "It is a tight game and didn't get the rhythm in our passing but two fantastic goals won it for us.
"The finish was great for Marcus Rashford's goal but there was quick inter-changing passing in the build-up. We did not do it enough because they are a handful to play against, they have to trust themselves more.
"It looked like Victor Lindelof kicks the ball first and it is a tight decision but probably the same on Anthony Martial. I don't think it was a penalty.
"When we go the second goal, that is when they started strutting about. It is tight scheduling but we cannot afford starts like this.
"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."