The 26-year-old stopper admitted that he was never overly optimistic regarding a call-up for the tournament.
"I didn't really think about it too much," Stockdale told fulhamfc.com. "There have been several goalkeepers who have continued to put in good performances this year; John Ruddy for example, Ben Foster even though he's retired [from international football], and Rob Green's been playing well.
"We've got Joe [Hart] already and Scott Carson has been playing well so I wasn't too expectant.
"In the future I just want to play as many games as possible and keep myself fit and if the call [from England] arises then the call arises."