United and City played out a dour 0-0 draw at Old Trafford that was short on entertainment as well as chances with both sides cancelling each other out.
United came closest to breaking the deadlock in the closing stages when substitute Jesse Lingard hit the crossbar and defender Chris Smalling forced a smart save from City keeper Joe Hart.
“It was a very tough game for both sides. We were unlucky, they were lucky,” Dutchman Van Gaal told the BBC.
“We had 90 minutes control of the game against a side like Manchester City. I cannot complain. But you want to win and we did not.”
Van Gaal felt aggrieved that his side were not awarded a penalty in the second half following a coming together in the penalty area between United midfielder Ander Herrera and City forward Raheem Sterling.
The United manager said the incident strengthened calls for the introduction of video technology.
“We should have had a penalty on Ander Herrera,” he said. “It is easy to see for me but I have a replay. The referee has one second.
“I always say we need the modern technology but I am the only one in the desert calling for it.”
City boss Manuel Pellegrini was happy to have claimed a draw at the home of their rivals but not satisfied with his team’s performance.
“I am satisfied with a point but I don’t like to play this way,” he said. “We are back at the top of the table.
“It was a very tactical game. I prefer to play in another way but we defended well.
“Unfortunately for the fans it was not a very attractive game. We are two creative teams but we could not do it today.”
(Reporting by Toby Davis,; editing by Pritha Sarkar)