Pep Guardiola’s men won the first leg 3-1 at Old Trafford three weeks ago, but Nemanja Matic’s first half strike made it a nerve-shredding affair at the Etihad Stadium. Manchester City eventually edged home 3-2 on aggregate.
Solskjaer became the third manager to win two away matches against Guardiola in his managerial career, after Jose Mourinho and Jurgen Klopp.
Even though the Red Devils failed to mount a comeback against their local rivals, the 46-year-old was pleased with the fact that his side have won twice against the English champions at the Etihad Stadium this season.
Speaking to Sky Sports after the game, the Norwegian coach admitted he is proud of his player’s performance.
"I am so proud of these players. They have beaten City twice at their ground. They have come so far these players. They have given me absolutely everything.
"We have come a long way. Even though we did not create too many clear cut chances we pressed them back. It pleased me.
"Of course it is hard to come here and score a goal with 11 never mind 10. It was never a sending off. Absolutely for me a joke. How many times did they foul us?"
