Saints finished in the top half of the top flight for five years running after Wright arrived in Perth, initially as assistant to Steve Lomas for his first season.
They have just missed out in the last two years and are four points off sixth-placed Hibernian with five matches before the split.
But Wright is not putting himself or his players under extra pressure after they were bottom of the league going into December.
They have only lost two league games since then, one against Celtic and the other a narrow defeat against Saturday's opponents, Livingston.
And Wright will remain satisfied if they consolidate their position but just miss out on the top six.
"It makes a big difference to all clubs because there's extra prize money," he said. "It's not EPL in terms of prize money but it's all relevant.
"You get one of the big two probably or, if you're lucky, the big two in terms of extra revenue when you get them at home games.
"It is important but it's not the end of the world if it doesn't happen. We have finished eighth and seventh and they are still good seasons for us.
"The main thing every season for us is staying in the league."
However, Wright is determined to do everything to give themselves a chance, starting with the visit of Livi.
"A win can help it," he said. "With games running out, wins are important.
"It will be a tough game, you saw them against Celtic the other night, they are a strong side, a physical side, but what gets overlooked, they have a lot of quality as well.
"They cause problems with long throws and direct balls into the box from set plays, and we have got to be ready for that.
"But we also have to look at it from open play, they have quality in terms of (Steven) Lawless, (Craig) Sibbald and (Scott) Pittman, who can hurt you from open play as well.
"They have a good mixture of being a physical team but they certainly know how to play as well."