The uncapped 23-year-old was injured before his March call-up to a 40-man provisional squad, and he was not chosen for this international break.
His Posh side have also fallen from the League One play-off places.
"My form since the call-up hasn't been great so it probably pushed me away from the squad," Forrester said.
"It's just about getting back to where I was at and enjoying it again - keeping myself in the eye of [Ireland manager] Martin O'Neill.
Forrester picked up an injury at Millwall on 20 February before returning on 12 March versus Port Vale and helping Posh win at struggling Doncaster on Saturday to end a seven-game winless league run.
"The injury probably knocked me back a couple of weeks performance-wise and the last two games I've been trying to get back to where I was at and am probably struggling a little bit," Forrester told BBC Radio Cambridgeshire.
"If I'd had a run of games before the main call up it could have been better for me."
He will be hoping to play for a Republic side wanting to improve upon their record from Euro 2012, when they went out at the group stage having lost every game.
"Seeing them play in the European Championships four years ago, didn't do so well and you're looking saying maybe I could be there someday," he said.
"I've got close but not close enough for my liking, but it's a step in the right direction and maybe one day I'll be involved and put the jersey on with pride."
Peterborough midfielder Chris Forrester says poor form and injury since a Republic of Ireland squad call-up has seen him drop away from the fold.