Anthony Martial scored United's first league hat trick since 2013 to ensure Solskjaer's men moved to within two points of Chelsea in fourth ahead of their game against Manchester City at Stamford Bridge on Thursday.
"At times it was very very good football but for me we could've and should've scored more goals and put the game to bed before half-time," said Solskjaer.
"It's worrying when you go in half-time knowing you should score two or three more goals but the control and way we pressed and stopped Sheffield United from playing as well was very good.
"Very pleased with the performance but still more to come. We shouldn't be 100 percent happy with it.
"We can see the connection between Anthony, Mason [Greenwood], Paul [Pogba] and Bruno [Fernandes] and we can create chances from those situations as well.
"We should've scored more today, little bit lackadaisical with the final pass. When we're in 100% shape we'll be better."
Liverpool and City are clear in the top two positions in the table but Leicester's two draws with Watford and Brighton since the restart has raised the possibility that third place may be up for grabs.
"I've never said fourth is our aim," Solskjaer said.
"We want to go up to third but we have to focus on each game as it comes and there's two cups for us there as well. One game at a time and in the end we can count the points and maybe have only two teams in front of you."
Against Sheffield United, who are yet to score in three games since the break, Martial was the star and took home the match ball for the first time in his senior career.
His hat trick also took him to 19 goals for the season, his best tally for a season since moving to Old Trafford in 2015.
I think the first goal, I think that's a vital goal as well today, but the way he turned and got himself into a position to score from Marcus' cross, I was very pleased with that one," Solskjaer said.
"He's getting more and more into those positions. He nearly got a goal against Tottenham as well, great turn and finish and great save by Lloris. Anthony's in good form. I'm very happy for him. Unfortunately he couldn't celebrate with fans."