The Gunners again achieved a top-four finish to achieve qualification to the Champions League for next season but Gazidis says that there is more goals ahead for the North London club who have gone seven seasons without silverware.
"It is important to reiterate that for everyone at the club, qualification for the Champions League is not our ultimate ambition," he told the club's official website.
"Our majority owner Mr Kroenke has made it clear that while it's an achievement to make the Champions League, our ultimate objective is to win the major trophies.
"We all share that clear ambition and will be driving the club forward to achieve it.
"Arsene and I have already been planning what we need to do to strengthen so we are better placed next season.
"One thing is certain - the club is in a very strong position to move forward and our form of losing just one of our last 16 Premier League matches shows that we have a solid foundation on which to build for success."