Villa remain just three points clear of the drop zone with four matches still to play and have a worse goal difference than relegation rivals Wigan Athletic, but Vlaar is confident they can stay up after limiting the damage at United.
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."