The Perth club have been the toast of Scotland since sending Rosenborg spinning from the Europa League.
The Northern Irishman is now turning his attention to Thursday night's third qualifying round first leg with Belarusian outfit FC Minsk, but he is not concerned about his players developing big heads after they shocked the Norwegian league leaders.
Instead, he believes the success has only whetted their appetite for more.
Wright told Press Association Sport: "There has been such a positive reaction to the Rosenborg result and I want the players to show me that they want more of it.
"Everyone loves a pat on the back and to see their names in the papers. If that fires them up to believe they can win again against Minsk, then that's great. It's important that we keep the run going."
Thursday night's first leg takes places in the city of Grodno, 140 miles west of the former Soviet state's capital, while Minsk's Dinamo Stadium is redeveloped.
Few fans of either side are expected to be in attendance for the match but an eerie atmosphere does not concern the Saints boss.
"We don't need to quieten the crowd because there won't be that many there," Wright joked.
"It's disappointing that there won't be many of our supporters there either but I think we just need to show the right attitude and make sure we don't relax.
"Players can focus a bit easier when there is a big crowd. But these lads have all played in pre-season friendlies and games in the middle of winter when crowds are low. I don't see it being a problem."