Saints have conceded just one goal in their last seven matches - a penalty against Burnley in the 3-1 victory at St Mary's on Sunday - and they've racked up three wins in their last four games to sit well placed in eighth place in the Premier League.
Forster says everyone should take credit for the good results but warned they've set the bench mark high for the remainder of the campaign.
He said on the club's website: "I think what we've done now has set the standard for how we need to play for the rest of the season and we'll have to try to replicate that in every game we play.
"We kind of said it last year when we went on a good run that it's all about the team and it's been the same for this run. It makes it easier to win games if you're not letting in many goals.
"I think we're all really proud of it. It's been a lot of hard work and we've performed really well in games and we've looked very strong at the back and that can only be a positive sign of things to come."