The France international was introduced in the 83rd minute before scoring the winner against the Austrian minnows with only a couple of minutes left on the clock.
The United manager praised the 24-year-old for not only his contribution on Wednesday night but also his hard work and commitment to bettering himself and the team.
Anthony Martial wrapped up the victory for Man United in their Europa League second-leg tie
In the post-match interview, Solskjaer said: ‘We needed to win the game. Of course, I wanted to but I couldn’t get all of [the substitutes] on.
‘We want to win and Anthony was begging to come on. But he promised a goal as well, so well done!’.
The Norwegian went on to praise his starlet’s contribution to the club, saying: ‘Anthony has upped his work-rate.
‘He’s working harder in training, he’s working harder in the games; his physical stats show that. He’s been an absolute joy to work with.
‘His attitude has been spot on and him and Marcus [Rashford] have found and hit off a really good relationship.’
Jesse Lingard scored the equaliser after United went 1-0 due to Philipp Wiesinger’s strike
Solskjaer chose to leave the likes of Martial, Marcus Rashford, Bruno Fernandes, and Paul Pogba on the bench for the second leg after going into the game with a 5-0 lead.
The Red Devils initially fell behind due to a stunning strike from Philipp Wiesinger, but went on to progress to the quarter-finals 7-1 on aggregate.
Jesse Lingard provided United with the equaliser before Martial came on to seal the deal for Solskjaer’s men.
The Frenchman got on the end of a pass from Juan Mata pass to then dribble into the box and slide home his 23rd goal of the campaign.
Ole Gunnar Solskjaer says Martial begged to come on, moments before scoring the winner
Thanks to Martial, the Red Devils have progressed to the quarter-finals 7-1 on aggregate
Man United are now set for a Europa League quarter-final against Copenhagen after the Danish side beat Istanbul Basaksehir.
Speaking of the challenge ahead, Solskjaer said : ‘I know Stale [Solbakken, their manager] really well. A good friend of mine.
‘I did my pro licence study with him in Copenhagen, so I know what there is to know about Stale probably.
‘And he probably knows what there is to know about me! I’m looking forward to it.’