Villa are 16th in the standings after a dismal start to their Premier League campaign. Gerrard was booed off the pitch by the club's supporters following their last match - a 1-1 draw at relegation-threatened Nottingham Forest.
"It is a fact that I have to win over the supporters," Gerrard told reporters ahead of Villa's league trip to Chelsea.
"From the first day I came here until the last day, whenever that may be, and I hope it is a long time, I'll continue to keep trying to win these supporters over and prove I am the right man for this job.
"I don't doubt myself because I believe in myself...You have to accept (the criticism), you have to be aware of it and use it to get yourself back in a better place."
Villa face fourth-placed Chelsea on Sunday.