Gestede was brought to Villa from Blackburn Rovers over the summer transfer window, but his start to life at Villa Park has not gone smoothly.
Villa have won just one of their first 13 Premier League matches, and they currently sit at the bottom of the table.
However, Gestede insists Villa are not prepared to give up – and he wants his teammates to fight even harder to ensure that they get out of trouble.
“We are in the Premier League and we have to do everything we can to stay there,” Gestede said.
"It won't be easy. We didn't start well but there are still plenty of games to play and plenty of points to take.
"Nothing is finished. We have to keep going. We have to keep working in training - and improve.
"We have a new manager in Rémi Garde. He has his plan in his head and wants to put this on to the pitch.
"We are going to improve. We will fight to get some points. We have to pick up some points and make sure we get out of this position."
Villa lost their latest match in the Premier League 4-0 to Everton, and they showed little signs of improvement.
Garde had the entire international break to work with his Villa squad, but the French boss failed to spark them into life.
As things stands, Villa are five points away from safety, and they are starting to get cut adrift in the relegation zone.