City won the round of 32 tie in Denmark on penalties after scores finished 2-2 at fulltime. City struck through Lakyle Samuel and then substitute Matty Warhurst, with Charly Gray also being sent off for the visitors.
City goalkeeper Oliver Whatmuff then took the stage, saving FCM's third penalty in the shootout before taking and converting the winning spotkick himself.
“I’m really pleased in terms of the sort of spirit we showed,” Wilkinson told City's website.
“I think as a performance overhaul we were probably quite disappointed with the first half, but were much, much better in the second half in terms of the way we approached the game and our mentality and mindset.
“That was really pleasing.
“When you go down to 10 men, you know it will be difficult and then you concede straight away to make it 2-1 for them but between that minute and the end of the game, we probably had more attacking threat than the opposition.
“So that was pleasing in terms of seeing the boys react in a positive manner and try to still go and win the game.
“In terms of the shoot-out, obviously you can prepare for penalties and it’s a topic we’ve spoken about over the last two or three years when we get to these games.
“I’m a believer that it’s not just luck, I think you can prepare for them. And the players need to have processes and strategies when they take a penalty like you do with anything else.
“So, it was a case of falling back on your individual process but it’s difficult as a coach because obviously you feel like you don’t have much control over the outcome.
“But I do know we’ve got some top penalty takers and Ollie as a goalkeeper I think really stands up in those moments.”