The Birmingham-based outfit have only managed to win four games so far and as a result are 19th in the table and two points from safety.
However, Dutch defender Vlaar has insisted that if Villa concentrate on their own results rather than what their relegation rivals do, they are good enough to stay up.
"This is not the time to be feeling sorry for ourselves. We have to concentrate on collecting as many points as possible from our remaining Premier League matches," he is quoted as saying by the Express & Star. "That is our only concern. We can't think too much about what everyone else is doing. What matters more than anything is our own performance.
"All our efforts much be geared towards climbing the table and erasing the defeats we have had.
"The fans always stand behind us and that is very important they do that until the end of the season in every game we play. I believe we can get out of the relegation zone."
Next up for Villa is a home encounter against West Ham United on Sunday afternoon.