Having secured a top six Premiership place for the third season in a row, the Northern Irishman has his sights set on finishing as high as fourth.
That means overhauling Dundee United's three-point lead on them and Inverness, who are two points ahead.
The first step would be defeating Aberdeen at Pittodrie on Saturday, having beaten the Dons to earn the Saints' cup final berth at Celtic Park against Dundee United on May 17.
Wright has been nominated for the PFA Scotland manager of the year award after guiding the Perth club to the Scottish Cup final, plus a run to the League Cup semi-finals, and two impressive away wins in the Europa League qualifiers.
And he has achieved this while slashing more than £200,000 from his playing budget.
"As a club, we budgeted to finish 10th because our budget was cut," he said. "Even though we were successful last year on the pitch, our gates went down and we had to make savings.
"But within this group, we made the top six our aim. I think we have improved this season and we are on course to surpass last year's points total."
He added: "So I think our league performances have been more impressive than our cup feats.
"So far we are more than satisfied with how the team has done, especially when you consider the injuries we've had.
"We've lost Steven MacLean for 19 games, Allan Mannus for a while, Steven Anderson for three months, Gary McDonald for six weeks and had both Murray Davidson and Tam Scobbie ruled out for the rest of the season yet coped really well.
"That shows our depth and how well we have really done to get into the top six."
Wright has been put forward for the PFA's manager prize but insisted if he wins, it will be reward for everyone involved in Saints' efforts this campaign.
"I'm proud but I'm also delighted for so many people who help me every day," he said. "It's always the manager who gets praise when things go well, but I've got Callum Davidson, Alec Cleland, Stevie Banks and a load of others giving me tremendous support.
"And you only get recognition if you have good players and I am blessed with a bunch of guys I can trust, so really it's recognition for everyone at the club."
Undoubtedly the pick of Wright's bunch has been 26-goal striker Stevie May, and Gordon Strachan is believed to be considering calling up the 21-year-old to his Scotland squad for next month's London friendly with Nigeria.
Wright said: "That's Gordon's choice and not for me to interfere in it, but I think Stevie is ready for a full call-up.
"A friendly at the end of the season could be the perfect opportunity for Stevie to be included. If it did happen, it would cap off a tremendous season for him."