The Dutchman bagged a treble inside 33 minutes on Monday night but that was as bad as it got for Villa who were able to escape any further costly damage to their goal difference.
"I knew it was going to be really, really tough," said Lambert. "But we kept on going and it was important we did not capitulate like we did at Stamford Bridge earlier this season, but congratulations to Manchester United.
"I am proud that my lads kept on going, credit to them, especially against the best team in the country.
"You want to give a good account of yourselves at Old Trafford but after the start we had you are not wanting to concede more goals. The lads kept on going and, for us, next Monday [against Sunderland] is the one we have to win.
"Manchester United have worked really hard for each other, they have a winning mentality and the best team always wins the league."