The 2-1 victory at Villa Park lifted Paul Lambert's side out of the bottom three of the Barclays Premier League, as well as confidence ahead of their next clash at Arsenal on February 23.
"It was big. We really deserved the win," said Vlaar, speaking on the club's official website.
"We realise that for ourselves and for the fans and every employee at Villa because we needed this so badly, and it finally happened.
"Everybody was very happy, and you could feel the relief in the stadium and in the dressing room.
"We have to go on. It is only one win and we want more. We have to look forward to the next game."