The Gunners ended a nine-year wait for silverware when they beat Hull City at Wembley in May - a victory that eased the disappointment of another underwhelming league finish.
Arsenal spent more than 100 days at the top of the Premier League last season but had to settle for fourth place, seven points behind champions Manchester City, who they face in the Community Shield on Sunday.
"When there's a lot of talk about a team that should or could be winning things and it's not happening it can become a little bit frustrating," Oxlade-Chamberlain said.
"There's been a little bit of negative media about Arsenal in recent years but we always believed we would win a trophy soon and the squad we're putting together could do it.
"The fact it did happen, I don't know if it was a relief, it was a really nice reward for the togetherness we've had to show for a while now.
"It does start a winning momentum and once you know you can win, it gives you confidence - you can go into competitions thinking you can win and expecting to go far."
Arsenal have been busy in the transfer market this summer with the signings of Alexis Sanchez, Mathieu Debuchy, Calum Chambers and David Ospina.
Sanchez, who scored 19 goals for Barcelona in La Liga last season, cost around £35m and is Arsenal's second most expensive signing after Mesut Ozil arrived for £42.4m last year.
"It's really exciting to see someone like Alexis Sanchez come in as well as Mathieu Debuchy and Calum Chambers," Oxlade-Chamberlain said.
"It definitely brings a really good lift to the squad - I feel it myself.
"When you're playing with new players like that you want to get to know them, try to impress them and you want to gel with them as quickly as possible.
"It does bring a massive lift of excitement to the squad and we haven't even seen Mesut Ozil yet - when our Germany World Cup winners come back it will give us another lift again."