The Dutch club, who have started their Eredivisie campaign with five straight wins, defeated Jose Mourinho's United 1-0 at De Kuip in their Europa League group stage opener.
Tonny Vilhena's 79th minute goal was the difference in the end in what van Bronckhorst describes as a difficult encounter for his players against a Red Devils unit who controlled large portions of the 90 minutes.
"United upped the tempo and used their physical presence in moments of the game, making it very difficult for us.
"But we knew that if we could keep the ball against Manchester, there are possibilities.
"In the second half you saw that Man United want to win with the tempo and the three substitutions, you sensed that they want to leave her with the win.
"At the right moment we scored the goal - a fantastic goal on the counter-attack.
"After that the spirit came in the team and the determination to be there for the last 15 minutes. We fought hard to get the result and after 90 minutes we did."