The Gunners overhauled a seven-point deficit on north London rivals Tottenham following their superb run-in, which was kick-started by a memorable victory at Bayern Munich as they bowed out of Europe.
While Arsenal still have to negotiate a potentially tricky two-legged qualifier in August before they can focus on a remarkable 16th campaign of Champions League football, Sunday's 1-0 win at Newcastle gave the club a completely different outlook from the one they faced after defeat at White Hart Lane on March 3.
Gibbs feels the confidence Arsene Wenger's squad will gain from the last two months can enable them to go the distance in 2013/2014.
"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 said in 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 insists no-one at the Emirates Stadium will be resting on their laurels of a fourth-place finish.
"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."
Wenger feels his side have gone some way to answering their critics following their end to what had been a frustrating campaign, which included the lows of cup defeats by Bradford and Blackburn, before a Champions League masterclass from Bayern Munich at the Emirates Stadium only to then outplay the Germans when winning the second leg of the last-16 tie.
"I believe that the last three months the team has shown we are ready [to challenge for honours] because we are consistent," Wenger said on Arsenal Player.
"The strengths we have built and the way the team has grown can be transferred into next season.
"That is very positive so let's keep the group together, rest well and come back in a strong way."
Arsenal will be proactive in the summer transfer market, with the free transfer of France Under-21 forward Yaya Sanogo from Auxerre expected to be the first of several new arrivals.
Wenger is understood to have targeted offensive additions this summer, with the likes of Fiorentina's Stevan Jovetic, Real Madrid frontman Gonzalo Higuain and even England forward Wayne Rooney all said to be on the Arsenal manager's radar, as is Borussia Dortmund defender Lukasz Piszczek and even Brazil goalkeeper Julio Cesar, who is set to leave relegated QPR.
Wenger, tough, warned finding the right man at the right price is set to be another test.
"There are many clubs out there with a lot of money, so the competition is very hard - there is not as much talent as money today in football," he said.
England midfielder Jack Wilshere is now set for surgery on his troublesome ankle.
While that will rule him out of the friendlies against the Republic of Ireland and Brazil, it should see the 21-year-old return fully fit for the start of the new season and the Autumn World Cup qualifiers.