John Stones capitalised on poor set-piece defending to quickly puncture a buoyant atmosphere at De Kuip and strike duo Sergio Aguero and Gabriel Jesus were on hand to pile on further misery inside the opening half hour.
England centre-back Stones completed the rout with a second header after the hour-mark and, although the Dutch champions produced a spirited showing in the second half, the damage had long since been done.
"After that early goal, City grew more and more in the game and we struggled to keep up with the high pace they played," Van Bronckhorst said.
"In the second half, we changed the system. We wanted to get more ball to get into our game, but that was difficult for this opponent.
"City is just one of the top teams in the world, we really had to have a good day to get a chance against them and we did not have that."
Captain Karim El Ahmadi was similarly crestfallen and conceded there was an element of stage fright about Feyenoord's performance on their return to the Champions League following a 15-year absence.
"The disappointment is very big," he told UEFA.com. "We have to be realistic that Manchester City were much, much better then us.
"The first goal was very easy and early in the game. If you can keep them a longer time at 0-0 you can get some confidence but, after going down 1-0 early, you could see we were afraid to play our game.
"The goals they scored were from corners in which we were not sharp enough."