Gibbs made 29 starts for the Gunners last season despite suffering some injury problems and the side signing Spain international Nacho Monreal from Malaga in January.
And the 23-year-old, while not part of Roy Hodgson's squad for the end-of-season friendlies against the Republic of Ireland and Brazil, insists his World Cup hopes will not interfere with his performances at club level.
Gibbs told Arsenal's official magazine: "It has been my best season so far. It is a stepping stone for me and now I just need to build and stay fit. I am sure I can do more for the team.
"I was hopeful of getting into the England squad this summer, but I was not called up.
"I will just relax now and make sure I prepare myself physically for next season, ensuring that I go into it with a clear head.
"I am really looking forward to it and hopefully we can all make it a special one."
Arsenal finished the 2012/13 season in fourth place, securing a place in the Champions League qualifiers after a ten-match unbeaten run.
And Gibbs believes Arsenal have what it takes to fight for their first piece of silverware since the 2005 FA Cup.
Gibbs added: "The dramatic finale to the season made us even stronger, and we will be going into the new one head on.
"We are aware that we need to produce next season and have to make sure we are confident about dealing with that expectation."