Saints began their competitive campaign on July 2, just five weeks after their final Premiership fixture of the season against Aberdeen on May 24.
Their foray into the Europa League qualifiers proved short-lived as they crashed out on away goals to Alashkert FC at the first hurdle.
In addition, Murray Davidson, David Wotherspoon, Chris Millar, Steven Anderson, Simon Lappin and Wright himself have all picked up knocks as they step up their preparations for the opening Premiership fixture.
Wright, who picked up a groin strain in the second leg against Alashkert, told The Courier: “We have to try and get boys fit and ready for Tynecastle next weekend. I can’t remember having so many injured at this stage of the season. Maybe it is just bad luck or tired bodies.
“We are all fit enough and the pre-season schedule was well planned. But maybe it is an indication that players’ bodies do need a bit longer break in the summer. We have to focus on Hearts and the league. Europe has gone for us.
“For once it would be nice to get off to a flying start. We usually don’t get going until September and I’ve no idea why we are slow starters. Hopefully we can get a few decent results in August to set us up for another good campaign.”