Martial shone in the match, which was the first behind-closed-doors fixture at Old Trafford, and while everyone raved about his third - which was a lovely chip past Simon Moore - Solskjaer was more impressed with the Frenchman's movement for the first goal.
"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".
"I think that he's now at a good age, that he has more experience".
Martial has scored 14 goals in 26 Premier League appearances this season, eclipsing his previous record of 11 goals in the campaign after he joined the club in 2015.
"We should've scored more today, little bit lackadaisical with the final pass".
Manchester United are set to take on Norwich City in the FA Cup third round at Carrow Road on Saturday afternoon. It is very important for him to score goals, ' he added.
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All the build-up to the contest centered around a potential partnership between Bruno Fernandes and Paul Pogba in the Red Devils' midfield, but Martial stole the headlines with a superb display upfront.
"I saw many pictures of our fans", the Serbian said of the 40,000 supporters pictured on the stadium wrap.
"If there are any good deals to be made and players who can make us better, of course we might have to spend some money on that but the squad is great to work with and it's moving in the right direction".
"I'm very happy for him, the first two he's in the box ready for crosses", Solskjaer said, as per Metro.
"He's getting into those positions more and more".
But Ole Gunnar Solskajer put his faith in Martial, who is enjoying the best scoring season of his career having reclaimed the number nine jersey.