Wright, who has signed a new three-year contract extending his stay in Perth until at least May 2017, insisted the Scottish champions' European reinstatement in place of Legia Warsaw will prove a huge boost.
St Johnstone kicked off their campaign with a 2-1 win at Ross County on Sunday and Wright, speaking to Sky Sports News, said: "It’s going to be a tough game, they are the champions and I think they will be hurting over the experience they’ve had in Europe last week.
"They probably get a massive lift in terms of the squad getting through again and we’re expecting a really difficult game. I think the new manager will be expecting his players to bounce back and put on a performance here on Wednesday."
But Wright is convinced his side are capable of pulling off a shock after goals from Michael O'Halloran and Steven MacLean got their season off to a winning start in Dingwall.
"I think you want your first points on the board and we always knew it was going to be a difficult game at Ross County, particularly coming off the back of a long trip in Europe on Thursday night," he said.
"We didn’t get back until the early hours of Friday morning and the lads responded really well. They were fresh, hungry, played really well and fully deserved the three points so we’re glad to get off the mark in our first game and we look forward to having Celtic here.
"We’ve done reasonably well against them over the last few years. Had a cracking game here last season where it was three-all so we’re looking for more of the same."
And Wright, who has set a target of a top-half finish this season, believes Saints will cope with the loss of leading scorer Stevie May following his move to Sheffield Wednesday.
"At the start of the season we set a target of the top half. A club our size will want to avoid being down there at the bottom of the table.
"We do have a smaller squad this season but over the last few seasons we’ve been sixth, sixth and third and if we can get top six again then it would be a tremendous achievement for the players.
"Stevie's departure is a blow. Anybody who loses their top striker with 27 goals for us last season will be difficult to replace but the season before we lost 28 goals from midfield, three players left and we replaced them with Stevie.
"We’ve got Adam Morgan in, Michael O’Halloran started the season well - scored a goal - and Steve MacLean.
"We created a lot of chances on Sunday but I’m also looking to bring in another striker so we just move on.
"We wish Stevie all the best, he’s been tremendous here for us and with Sheffield Wednesday they’ve got a very good young player.
"I sat down with the chairman mid-January and we looked at the squad and normally we let contracts run out and wait to the summer but the squad was doing particularly well.
"We decided to sign as many as we could, and extend their contracts so really in the summer we were only looking to bring in one or two players, and that’s still probably going to be the case.
"We brought Adam Morgan in to replace Stevie May at the minute. We will look to add to the squad but continuity is vital to us."
Watch St Johnstone v Celtic live on Sky Sports 5 from 7.30pm on Wednesday.