United sit second in Group B ahead and are yet to secure a place in the round of 16 ahead of their clash on Tuesday against Wolfsburg.
But even if they do progress to the first knockout stage, the Dutchman has suggested they need to strengthen further to be in with a chance of competing with the likes of defending champions Barcelona.
"I don't think that we are able to win the Champions League now," he told reporters. "Maybe next year when we strengthen our selection again.
"We can beat anyone on our day, but normally we are not good enough to win the Champions League, but we shall try to do everything."
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United go into the match in Germany on the back of a 0-0 draw at West Ham and are at risk of elimination if they fail to win.
"Yes, we can win on Tuesday," Van Gaal added. "In every match we create chances and we have actually created more of them in the Champions League than in Premier League games.
"But playing on Saturday, resting on Sunday and travelling on Monday is not ideal for a Tuesday match but we have to cope."