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Martial's first treble in senior football - also the first by any United player in the Premier League since Robin van Persie more than seven years ago - was just reward for a fine showing from the hosts, as the Blades laboured in the Manchester heat.
It could have been a more commanding margin of victory, with Marcus Rashford culpable for a pair of glaring first-half misses, and it was this area of his side's performance that drew Solskjaer's attention as much as Martial's brilliance.
"The build-up into the last pass or finish was good, but we need to do better with all the spaces we created," he told Sky Sports.
"I do expect them to take those moments. It didn't cost us today. We know we played well but we can do so much better.
"There's been games where we have dominated and not taken our chances, so we need to take our chances – that's what I'm saying.
"We created enough to win by more and in other games we've created enough to win them but not taken them.
"We need to take the chances and on the last pass be aggressive and progressive enough with our passing."
Aaron Wan-Bissaka assuaged doubts over the attacking side of his game with a superb assist for Martial's second in the 44th minute – a pivotal moment in the contest given Sheffield United had resumed brightly from the first-half drinks break.
"He's a former winger, he had another couple of great crosses as well. We need to be on the end of those," Solskjaer said.
"Aaron is developing all the time. He's not played full-back many years and he'll only get better."
Paul Pogba turned in a polished performance on his first start since September, operating alongside Bruno Fernandes and Nemanja Matic in a United midfield three that appeared ideally balanced.
"Paul was quality out there. He settled us, good decision making, good passing, hard to take the ball off him," Solskjaer added.
"I'm very pleased that we can get more minutes into him and let's see what we do in the weeks coming."
Wednesday's victory extendedthe Red Devils' unbeaten run in all competitions to 13 matches.