The Red Devils' boss conceded the Merseysiders deserved their victory on home soil but couldn't hide his frustration at the manner of how they scored their goals
Daniel Sturridge converted a 20th-minute penalty before Roberto Firmino scored for the third game in succession after the break, with United indebted to goalkeeper David De Gea for preventing a rout in the first leg of their last-16 tie at Anfield.
United were second best against the bitter rivals throughout but although the Dutchman agrees Liverpool were worthy winners, he believes both of their goals were debatable.
Van Gaal argued afterwards that referee Carlos Velasco Carballo's decision to award a penalty for Memphis Depay's foul on Nathaniel Clyne was questionable and felt Liverpool also should have been penalised for offside in the build up to Firmino's goal.
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"They played very good in the first half and we could not cope with their pressure," Van Gaal told BT Sport. "They had chances but David de Gea was fantastic.
"It is a cheap penalty. The referee cannot [award the penalty] because I think that [Depay] holds [Clyne] outside the box and then he is falling down. It is not because he is kicked by Memphis - but it is difficult, you cannot see that in one second.
"Liverpool deserved their goals but how their goals are existing - I see how they scored their goals.
"In the second half we changed the shape and we had much more contribution in the game but we didn't create many chances and they scored another cheap goal.
"That's difficult because 2-0 is a very difficult result for us. I've seen the videotape [of the second goal], I think also that the guy [Jordan Henderson] who gives the pass from outside was already offside."