The Red Devils brought a two-nil lead into the second leg and were expected to have it easy against the La Liga outfit.
Manchester United started brightly to dent the visitors’ hopes of mounting a comeback when Edinson Cavani got the lead just six minutes into the game.
The Red Devils kept Granada at bay throughout the game and doubled their lead during the dying embers after defender Jesus Vallejo scored an own goal.
“Granada do give you a game. It's a physical game, they throw people forward. You have to defend in these kind of games,” Solskjaer said after the game.
"2-0, clean sheet, some good individual performances. We're full of confidence going into Sunday [against Burnley]."
Paul Pogba was taken off at half-time after picking up a yellow card, and Solskjaer said he did not want to risk.
He added: “Sometimes, Paul wants to win so much... he went into a couple of tackles after his yellow card but I thought I don't want to risk that [him being sent off] even though he played so well. We missed three [through suspension]. The season has been hard enough as it is."
Manchester United will be facing Serie A side AS Roma in the semi-finals.
The Norwegian coach concluded: "I've not seen too much of them. I knew they played two good games against Roma. They defend well, as Italian teams always do. We all know Edin Dzeko so every ball into the box is a dangerous one.
"We are looking forward to it. We're in the semis. It feels like a proper European tie because Roma is a club with lots of history. We've done well against Italian sides before.
"We're going into it hoping to get to the final. If we can finish the season with a trophy that'd be great."
