Solskjaer insisted his side were only good for the opening 20 minutes of the game but was happy to have qualified for the next round of the competition.
The Red Devils took the lead in the fifth minute when Scott McTominay, who was captaining his boyhood club for the first time, bounced a header into the roof of the net.
The Scottish international's goal proved to be the match winner as both sides lacked the cutting-edge to convert half chances.
"After 15-20 minutes it seemed like a balloon popped, they came into the game and we gave them confidence, they gave us a good game,’ Solskjaer told BT Sport after the game.
“The most important thing in the cup is that you go through so that will make everyone happy but the first 15-20 minutes I think were the highlights of our game”
“I think we played some very good stuff, created chances and then we let them back into the game but we are through."
"We started giving them the ball back easily and we started to complicate it. Maybe we had one or two out of position and then suddenly they counter attack.
"And when you've got Andre Gray and Ismaila Sarr running at you it puts your heart rate up!"
Next up for Manchester United is a trip to Turf Moor to face Burnley in the Premier League.
