United raced into a 3-0 lead, with Robin van Persie grabbing a hat-trick inside 33 minutes, but Villa improved after the break and prevented the newly-crowned champions from adding to their lead.
Vlaar insists his side must draw confidence from their second-half display if they are to avoid slipping through the relegation trapdoor.
Villa slumped to an 8-0 defeat at Chelsea in December and Vlaar feels his side did well to avoid another capitulation at Old Trafford on Monday, as goal difference could well be crucial to their survival hopes.
The Midlands side are currently three points above third from bottom Wigan but the Latics have a game in hand and a superior goal difference, with Villa on -27 and Wigan -23.
Vlaar is well aware that the tight nature of the Premier League could lead to goal difference coming into play on the final day of the campaign, when Villa travel to Wigan.
He said: “It’s a positive thing. We all know what happened at Chelsea and it didn’t happen this time. Some people expected it but it’s an improvement.
“The second half was a lot better, we had better positions, we didn’t lose possession and kept the spaces a lot smaller. It was more difficult for Manchester United.
“We are four goals behind Wigan so we have to get enough points. Everyone feels responsible.”
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