Partizan Belgrade proved tricky opposition in Serbia a fortnight ago, but United made light work of them on Thursday evening to reach the last 32 with two Group L games to spare.
United's improved attack was key to the 3-0 victory at Old Trafford.
Having mustered just one shot on target across their previous two Europa League matches, they had seven against Partizan.
Mason Greenwood, Anthony Martial and Marcus Rashford all scored classy goals as Solskjaer's men showed attacking bite.
"Very happy," Solskjaer said. "That was the reason we played the three of them as well. We felt if we played a strong team and created chances, we needed players out there to take them.
"I am very pleased with all those finishes. All three goals were high class. Of course we should have had quite a few more as well, but the first one settles us down I think.
"Mason - great composure, keeper goes early so he just changes his mind so very happy with that one. Anthony - that was probably the skill of the night, that goal.
"And Marcus, I am very pleased he scores with his left foot because he'll need more goals with his left foot because he comes in from that position quite often, so he can go inside and outside of the full-back."
It was an impressive show of attacking strength from United, who displayed the fluency and edge too often missing from their play this term.
"This is a little bit of a template on how we want to play, definitely," Solskjaer said. "But of course it's the opposition that allows you to play this way as well.
"No disrespect to Partizan, but they gave us spaces. Of course after we scored the first goal, they went forward.
"But that was pleasing for me, that we went forward, and needed the second and third because too many times we have been 1-0 up and haven't gone for the second or got the second.
"But it's learning, these boys are learning. Tonight will give them loads of pointers of how to play, how do we play when we're performing well even though the opposition is not the same as in the Premier League it was still good principles."
The only negatives on Thursday appeared to be knocks sustained by Scott McTominay and Harry Maguire.
Midfielder McTominay told the PA news agency he "should be fine" for Sunday's match against Brighton after picking up a foot complaint, while defender Maguire appears fine having completed the match despite a second-half issue.
"I think Harry will be OK," Solskjaer said. "He finished the game anyway. Scott is more of a concern, so let's see how he recovers in the next few days."