After City claimed a 3-1 first-leg win, Matic opened the scoring in the second leg to give the Red Devils hope of a comeback, only for the Serbia midfielder to be sent off for a second yellow card in 76th minute.
Playing with 10 men, United struggled to push effectively for an equaliser as Pep Guardiola’s side managed to book their place in a third straight Carabao Cup final despite losing the match 1-0.
Speaking post-match, Solskjaer was adamant his side did not deserve to be punished with the red card, while also stressing how proud he was to see them defeat City for the second time this season.
“It’s hard to come here and score a goal with 11 men, never mind 10. So it was never a sending off, absolute joke for me,” Solskjaer told Sky Sports.
“It’s ironic really he gets a yellow card for his first foul, almost gets a yellow on his second foul which isn’t even a foul and then the second one, the last one, is a yellow but nowhere near [a red card].
“How many times did they foul us? How many times was Dan James fouled? How many in the first half on Jesse [Lingard]?
“It’s the first question you’ve asked and it shouldn’t be because I’m so proud of these players. They’ve beaten City now twice in six weeks at their place. We’ve come so far with these boys, they’ve given absolutely everything.
“We wanted to be in the game with five minutes to go. That has to be your game plan when you’re 2-0 down. We’ve done that before and when we got that one [goal] we just needed a moment and unfortunately we couldn’t capitalise.
“These boys have come a long way. They’ve developed. Second half showed as well that even though we didn’t create too many big, clear cut chances, we pressed them back, we had spells where they were defended deep which pleased me.” City will now face Aston Villa in the Carabao Cup final to be played on March 1, while United are next in action against Wolves in the Premier League on Saturday.