Mikel Merino came off the bench to score twice late on as the Gunners won 2-0 today.
Van Nistelrooy said afterwards: "It was a game of thin margins. Of course, Arsenal was in a way the dominant side.
"We did well controlling them and on the ball we had our spells. The turning point in the game was their goal, but that's also what I mean by thin margins.
"The ball across from Ayew to De Cordova-Reid where he can tap it in.
"You start to react and go for a goal but then they score the second.
"I can only give credit to the players. We defended well as a team, we blocked a lot of shots, we tried to apply as much pressure on the backline.
"I think we were compact and strong.
"But overall, I can only compliment the team.
"We know that we are not scoring two or three goals every game. We get our goal and sometimes two, but we were creating against an Arsenal team who are in great form and contending for the title.
"It is the Premier League and it can be decided in the blink of an eye. Top quality players making a difference in the game.
"Of course, if you don't take anything from the game then there is big disappointment. We are close in getting results."
On James Justin's injury, he added: "We have to assess and he couldn't carry on.
"Hopefully it's nothing bad."