With four matches left to play, Villa are one place and three points above the relegation zone, but they have played one more game than Wigan Athletic in 18th.
However, having claimed a couple of positive results in recent weeks, Vlaar has expressed his confidence regarding his side's survival chances.
"Aston Villa can't and won't drop out of the Premier League," the Express & Star quotes the Dutch international as saying.
"We have won some games against our relegation rivals in recent weeks through sheer character and that is something that did not happen before the turn of the year.
"We are now under severe pressure. A win feels extra sweet when we have had to dig deep physically for it."
Vlaar signed on at Villa Park last summer from Dutch club Feyenoord.