The Villains are unbeaten in their last four matches in all competitions.
Remi Garde's men are currently 10 points off safety in the Premier League, but they go into their Midlands derby with West Brom this weekend on a four-match unbeaten run, and Gestede explained that the squad had not given up hope of pulling off a stunning escape act.
"We're earning points bit by bit," he told the Mail.
"There are a lot of points up for grabs.
"It's easier when you start picking up results. It helps you believe.
"Now we're doing that so our confidence is getting stronger and stronger.
Although it must be pointed out that two of the games in their recent run saw them go up against League Two side Wycombe, the Villains also collected an impressive point against high-flyers Leicester City and a vitally important win against Crystal Palace.
With so much ground to make up however, it is still essential that Villa collect some kind of positive result from the clash against the Baggies. But with the fixture pitting two local rivals against each other, the game at the Hawthorns promises to be a tight affair which neither will want to lose, meaning that it may perhaps come down to the smallest of margins that decides whether Villa's run continues for another week.