The Gunners won eight of their last 10 league matches to overhaul a seven-point deficit on north London rivals Tottenham and claim a top-four spot.
And Gibbs believes the confidence Arsene Wenger's side will gain from the run-in, coupled with the successful manner last summer's signings have settled into the side, will help them challenge next season.
"We would have liked to have had a better season, but I think overall you have to be happy with the way the team got back together after December and showed real character, yet again, to come back and finish where we want to be," Gibbs told the London Evening Standard.
"We were a new-look side for another season, again, with new signings that have had to come in and step up.
"It is never easy to just come straight into the Premier League and perform like some of our good players have.
"In the end, there was a combination of us needing to realise what we wanted from the season and the players starting to get to know each other more. As time went on, we started to gel.
"That was important and it puts us in good stead for next season because I believe the team have gelled because of this.
"The dramatic finale makes us even stronger and we are going into next season head on."
Gibbs admits that Arsenal have let themselves down in the knock-out competitions this season but believes they are ready to end an eight-year run without a major trophy.
"We haven't shown it consistently enough in the cups and the league, but you have seen many glimpses of what the team are capable of," the 23-year-old added.
"We have to focus on every detail to give ourselves the best chance to produce something because we are desperate to win a trophy."