Earlier this season, the Danish outfit admirably finished above both Manchester United and Galatasaray in the group stage to progress to their first Champions League knockout match for over a decade.
However, Copenhagen were unable to thwart the dominant force of Man City in the last 16 and lost both home and away ties by a 3-1 scoreline, including Wednesday's second leg at the Etihad Stadium.
The Citizens raced into a two-goal lead inside the opening 10 minutes courtesy of strikes from Manuel Akanji and Julian Alvarez, the latter's goal aided by a goalkeeping blunder from Kamil Grabara, before Mohamed Elyounoussi pulled one back for the visitors just before the half-hour mark.
Erling Haaland then restored City's two-goal cushion on the night and four-goal lead on aggregate with a clinical left-footed strike on the stroke of half time to help the hosts cruise into the quarter-finals for a seventh successive year, breaking two Champions League records and extending another in the process.
Neestrup was in charge of Copenhagen last season when they faced Man City twice during the group stage, losing 5-0 at the Etihad before playing out a 0-0 draw on home soil.
The 35-year-old stated prior to Wednesday's last-16 contest that the Citizens play "a level or two up" from their previous opponents in the group stage, and he reiterated his opinion after the match, confidently stating that the holders have all the attributes to go all the way and lift the trophy again this season.
"[Man City] are going to win it, they are." Neestrup told TNT Sports. "I think we have played three very, very good teams (in the group stage), but this is just a level up in everything.
"I have big respect for them. I think the group we were in was very, very difficult and we did a great job, but this is just a level up, it's just how it is."
In his post-match press conference, Neestrup added: "What I also take with me after playing City now in two games is they work hard. They work f**cking hard and they are physically strong.
"They're improving. They have top players, the structure they have is incredible. But it's not all 'chop chop chop' teams that does that. So it's not just the football knowledge, the football brain, the technical part, but they work hard."
Despite cruising to victory, Man City boss Pep Guardiola has commended his side for beating a "difficult team" in Copenhagen to advance to the quarter-finals.
"We scored two goals and that helped us a lot. I said to the players after the game, 'I would not convince you, I am going to tell you we went through against such a difficult team'," Guardiola told reporters.
"Copenhagen played United, Bayern Munich and Galatasaray. They are a difficult opponent. So well organised. And, of course, to be part of the titles we need everyone.
"That's why we used [our squad]. Really pleased with the performance. The people expect a lot of things, but I know how difficult it is.
"For another year we are in the best eight teams in Europe. The draw, next Friday, we will be there. Incredibly happy we are still in all competitions."
Man City, who have put together a 20-game unbeaten run in all competition, shift their focus back to the Premier League title race as they prepare to lock horns with leaders Liverpool at Anfield on Sunday.