The Gunners have finished as runners-up in the past three Premier League campaigns but the Brazilian defender believes that the team have learnt from their mistakes and can go one better this term.
Gabriel, who signed a new contract keeping him at Arsenal until 2029 last month, said: "I only have one thing to say, and Mikel (Arteta) says it: We are ready to reach new heights this season.
"I don't think we can give excuses; we did everything we could in the last three years. I feel like we had a little bit of bad luck sometimes, but we all believe that we can win big titles.
"The pre-season has started. We're focused on what our manager is telling us to do, and what we have to do, and what we have to improve. I think this year will be different."
Gabriel was reportedly a target for several clubs in the Saudi Pro League before committing his future to Arsenal and explained that he was only focused on his current side.
He said: "I didn't hear about anything personally, I didn't receive offers. A lot of people like to say things on the internet. I am focused on Arsenal. That is why I signed the contract that I signed and I am focused on the club.
"I've been at the club for five years now and I've seen how much the club has grown. I am here to win big titles and I do believe that this season will be different. We have let a couple of titles slip through our fingers recently. We almost won but I think this year, things will be different. I have a lot of faith in that."
Gabriel's season ended early last term after he sustained a hamstring injury in April, but the defender expects to be ready for Arsenal's opening Premier League game next month.
He said: "I am improving a lot. I already feel really good. I have been training really hard with the group already. The season is going to be full of challenges but I already feel good to hit the ground running and play."