In the Perth side's last two fixtures they have drawn 2-2 with Rangers at McDiarmid Park in the Ladbrokes Premiership and narrowly lost 1-0 at home to champions Celtic in Sunday's William Hill Scottish Cup quarter-final tie.
St Johnstone are in eighth place in the table, behind Kilmarnock on goal difference and still harbouring hopes of a top-six spot.
However, Wright in assessing the trip to Paisley, noted that his side lost 2-0 away to the third-bottom Buddies in October before a goalless draw in Perth in December.
He told SaintsTV: "They are different games. We did cause Celtic problems, we had 11 shots to their 16 which against a team of that quality, is pretty good.
"So we didn't only show resilience, we played good football at times, some really good counter-attacking football and felt we did enough to earn a replay but that didn't happen.
"Those types of performances should give you confidence.
"But it is a different proposition. I am hoping that when we go to St Mirren we don't give up as much possession as we do against Rangers and Celtic and with that comes a different game plan from our point of view.
"We haven't beaten them this season so that is one thing that we should be wary of.
"They are in a decent run of form, they have become a side really difficult to beat, difficult to break down and they have quality, particularly Ilkay Durmus in the wide areas and they have goals from midfield.
"It is difficult. It is a different proposition, in terms of what I said about Rangers and Celtic but it still going to be a tough game."
Wright concedes that the next three games against St Mirren, Livingston and Hibernian, the latter two of whom are above St Johnstone, will be key to their league placing.
The Northern Irishman said: "We have to take as close to maximum points out of them as possible to give ourselves an opportunity when we still have enough games.
"We can't afford to drop too many points over the next six games.
"You can put pressure on by winning tomorrow night and hopefully results go well for you, and you can put pressure on by taking points off Livingston."