Henry is hopeful that the club can use the success of back-to-back FA Cup victories to create a platform where the team can progress in the Premier League and the Champions League.
The Gunners will be one of the favourites to win the league next season if Arsene Wenger adds well to his squad and the club will be aiming to get past their traditional obstacle of the last 16 in the Champions League.
“Our generation started by winning the cup and went on to win a double and stayed unbeaten - that is all I can hope for this group to do,” he said.
“We would obviously like to prepare ourselves for possibly for a better campaign in the Champions League and the Premier League.”
Arsenal built some useful momentum in the Premier League over the second half of last season, which they need to try and replicate when the new season gets underway.
At one point they looked like the team most likely to push Chelsea for the title but they eventually slipped into third place.
A good start next season is very important and hopefully Wenger can tweak his squad options, giving himself a selection dilemma in all areas of the team.
As Henry mentions to Arsenal Player, a better campaign in terms of the Champions League is also important.
Arsenal disappointed against Monaco last season, heavily defeated in the first leg of their last 16 tie and it’s a competition that Wenger would love to win before he calls time on his career.
Not many people may genuinely believe that a Premier League and Champions League double is possible with Arsenal but it’s dangerous to write them off.