The Gunners' fine start to the season took a road bump on Monday thanks to a 3-1 loss to Liverpool at Anfield.
And Bellerin says the current Arsenal crop will not accept the defeat lightly.
"The dressing room is frustrated," said Bellerin. "There is a hunger in this team that wasn't there the last few years and we want to win every single game.
"We knew that coming here all the odds were against us, but the team believed that we could come here and get a result.
"For us to not get that is very frustrating, but we know we have another chance on Thursday to redeem ourselves [against Liverpool in the Carabao Cup].
"So we are not going to let this get to us. We have been working really well, we have been getting results that people didn't even believe we could get and, building on from the end of last season, I think the team is working really hard.
"I think when you build a new identity, a new way of playing football, it's not something that happens overnight. It's something that takes a lot of time.
"Every game we understand each other more and I am very positive about what this season holds for us."