
Bournemouth were much the better side, and while they were helped by a red card for Milan captain and goalkeeper Mike Maignan, they were in complete control throughout the 90 minutes.
Rose was thrilled with the result, saying: "A big night for us.
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"I'm quite happy for the club, for our fans especially, and really proud of my lads.
"The way they did it today was just brilliant from the first minute until the last minute.
"Yeah, we played a really good game."
(Image: Richard Crease)
Dissecting the game, Rose was pleased with how his side started and remained on top even when Milan had their full complement.
"Even with 11 against 11 we started well," he said.
"We put the pressure on them, we won balls, we created the chance. We got one penalty out of a big chance, a header from Hilly.
"And then the red card, of course, it makes something with the game. We are one player more. Sometimes you get in trouble in this kind of situation, but like on Sunday we did it with one player more really, really well.
Marco Rose (Image: Richard Crease)
"We just suffocated them. We didn't give anything to them and that's really good."
Rose said the message at the break was to continue to be dominant and not give their opponents a sniff of getting back into the game.
"Yeah, staying sharp, staying clinical," he said.
"I think after 45 minutes in the first half we had a situation where we gave an easy ball to the opponent with a not so good pass.
"And it was just about controlling the game.
"We were talking about the structure we wanted to do it with and we did it really well, really good.
"We knew that we have to control the counter-attacks.
"And as I said, we just suffocated them and scored a nice third goal.
(Image: Richard Crease)
"And that's why I'm quite happy with the performance tonight."
Rose admitted he was not looking for Bournemouth to try to keep possession and stop creating in the second half, explaining that passive football does not fit the identity of his side.
"It could be smart, but it's not us," he said, when asked if that was something he considered asking the team to do.
"So this is the problem and I don't want to give that impact, because then we could get in trouble.
"Maybe it's the next step for us to just control the game, to just finish it with possession.
"But I love my boys. I love our approach. And yeah, it could be the next step."