Mohamed Salah scored twice for the Reds, one to give them the lead and one to level matters after Mason Greenwood and Marcus Rashford had teed each other up for strikes - before sub Bruno Fernandes hammered in a free-kick to send United through to face West Ham United.
Solskjaer has previously acknowledged that the ideal scenario is, of course, to not fall behind in games as frequently, but the Red Devils have shown remarkable resilience to come back and win several times this season and he felt the more adventurous nature of the cup tie allowed that to happen at Old Trafford on Sunday.
“Both teams wanted to win, the [Premier League] game last week was more tentative,” he told reporters at full-time.
"Our message to the boys was to go for it, we have to be more positive. It’s a cup game so relax, don’t think about the league position and enjoy it.
“It’s a very good mentality to have to not give up. I didn’t think there was a lot in the game, we had a half a chance and played through us but our reaction was good.”
Fernandes was left on the bench as Solskjaer made a couple of changes to his starting line-up, allowing Donny van de Beek to come into the side, but the Portuguese attacker was called upon for the closing stages and hit the winner with a set-piece - which his manager revealed he had been working on in training.
"You never know if the keeper is going to make a save but because Bruno wasn’t starting today he had some time to practice - I never let him - but he stayed out for half an hour, 45 minutes practicing free-kicks with the subs and it worked.
“We’re delighted, we’re through in the cup and the next round is at home. The schedule is relentless but we want to do as well as we can in every game.”
United’s next game is against bottom-of-the-table Sheffield United, before a tougher-looking run against Arsenal, Southampton, Everton and the Hammers in the cup.