Romelu Lukaku and Marcus Rashford netted at St James’ Park to sink Newcastle in a 2-0 win.
Solskjaer has now won his first four games in charge of United after replacing Jose Mourinho at Old Trafford.
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The win leaves the Red Devils sixth in the Premier League, three points behind Arsenal in fifth.
However, United looked sluggish in the first half, with the Red Devils struggling to create clear-cut chances.
And Solskjaer, who watched his side pick up their first clean sheet, says United’s first-half performance wasn’t good enough.
He said: “Finally we kept a clean sheet. A very professional performance.
“We didn’t hit the heights that we can do but we were in control, kept plugging away and got the goals.
“A good first touch from a sub! When you see big Romelu Lukaku running towards you, as a keeper you might take your hands away!
“We were sluggish in the first half, it was like a testimonial, too many square passes.
“We go to Dubai after the FA Cup game, you need that fitness work because we will need legs come the end of March.”
United impressed in the second half at St James’ Park, with the Red Devils netting both of their goals after the break.
Lukaku came off the bench and scored once again, with the Belgium international bagging in both games under Solskjaer.
The striker tapped home after Martin Dubravka fumbled Rashford’s free-kick.
And Solskjaer compared Rashford’s dead-ball technique to United icon Cristiano Ronaldo after the game.
“You’d be happy with four wins from four – we haven’t conceded from open play yet either,” Solskjaer added.
“We were slow in the first half but we controlled the game well, we concentrated and overall it was a very professional performance.
“In a five-minute spell we gave them two or three chances but then we settled down again. Newcastle is a fantastic club, fantastic crowd, you expect them to attack you but Victor Lindelof and Phil Jones were fantastic.
“Marcus Rashford has the Cristiano hit, it swerves everywhere, but I liked his goal today. Calmed himself down, just passed it in. Well done.
“He is only 21, you have to remember that. You need to rattle Paul Pogba at times to get him going, he has been immense for us.”
United star Lukaku, who struggled to find form under Mourinho, was also vocal after the win, claiming the Red Devils are getting used to life under Solskjaer.
He said: “You have to be ready as a sub, that’s what the manager asks of me.
“I knew that the goalkeeper might fumble it, you have to gamble.
“It’s totally different with the new manager, we are all learning from him, so far so good.”
United are back in action on Saturday against Reading in the FA Cup.