The Perth side followed up their remarkable success over Rosenborg by beating FC Minsk 1-0 in Grodno in the first leg of the third qualifying round tie.
Steven MacLean's 68th-minute strike means Saints will now return to McDiarmid for next week's second leg with a precious away goal.
But Wright accepted his side had been forced to graft in order to secure the victory.
He said: "I don't think we reached the highs that we did in beating Rosenborg in terms of performance. We were workmanlike.
"It was quite warm out there and very sticky and a few of [the boys] looked a bit heavy-legged.
"But they only really caused us problems on the counter-attack. They were not breaking us down.
"It wasn't pretty, because they are not a pretty side to play against but we got the result we deserved.
"We knew they were not technically better than Rosenborg but had pace up front.
"However, I will repeat myself - it is only half-time and we will not take anything for granted."
St Johnstone were not put under too much pressure by the home side and built on their comfortable start to snatch a first-leg lead with MacLean's fierce hit midway through the second period.
The former Aberdeen and Sheffield Wednesday striker collected Liam Caddis' pass before taking advantage of space to shoot early on the right-hand side of the box, burying the ball under Minsk goalkeeper Vladimir Bushma.
Wright saluted the forward for his clinical finish and his work-rate.
"It was a classic striker's strike," Wright said. "Steven has taken it well and hit it across the keeper. You know what you get with Steven. He probably doesn't get as many goals as he should because of all the work that he does outside the box for the team."
The Northern Irishman also picked out teenager Caddis - making his first start for Saints since September 2010 - for praise and welcomed back Murray Davidson after the midfielder signed on again with the Perth club last week.
Wright said: "Liam Caddis for me was another who was excellent. He's 19 years of age and hasn't started a first-team game for 18 months. He had a very good performance.
"Unfortunately we lost Gary McDonald when his back went into spasm during the game. Murray has come on and does what Murray does. He is a good footballer. I'm just glad that we got him signed last week because he did well when he came on."
MacLean bagged the winner with 22 minutes left in Grodno - 140 miles west of the former Soviet state's capital, where Minsk's stadium is being redeveloped - to put Saints on course for the play-off round.
Netting the goal that booked Saints' place in the third qualifying round was not enough to keep Stevie May in the starting line-up as boss Tommy Wright opted to pack his midfield instead.
The 20-year-old striker - who struck the second-leg equaliser against Rosenborg - was replaced by Liam Caddis, while Murray Davidson took a place on the bench after re-signing with the club last week.
Visa delays and sky-high air fares meant the Scots travelled behind the former Iron Curtain with just one solitary supporter for backing.
But despite having to go it almost alone, the McDiarmid men coped well during a relatively trouble-free first 45 minutes.
Minsk did threaten within the opening moments, however, as their favoured counter-attacking approach conjured the first chance.
Roman Vasilyuk teed up Nikita Bukatkin with a rolled cut-back but his drive from 22 yards was off target.
Saints were not slow to get on the front foot either and Steven MacLean brought out home keeper Vladimir Bushma's first save on 12 minutes as he turned Dave MacKay's cross goalwards.
The visitors were able to get their foot on the ball as they hogged much of the possession but breaking down Minsk was another matter.
Bushma had to punch clear from Tam Scobbie's cross as David Wotherspoon lurked at the back post while Nigel Hasselbaink tempted Minsk right-back Aleksandr Sverchinski into collecting the game's first booking with two fouls inside as many minutes.
A Milos Rnic trip on Wotherspoon seven minutes before the break set up MacKay to pick out Hasselbaink with a free-kick but the Dutch forward shot straight at Bushma.
Minsk midfielder Sergei Kozeka saw a decent opportunity blocked by Steven Anderson just seconds into the second half as the centre-half bravely stood his ground.
Davidson's return to the Saints side came just four minutes after the restart and the Scotland cap made an immediate impression, coming close with a pair of headed opportunities.
Bookings for Wotherspoon and MacKay gave St Johnstone reason to be wary as Polish referee Marcin Borski proved to be overly officious but an offside flag soon came to Wright's side rescue as Dmitri Gorbushin looked to gallop through on Allan Mannus in the Perth goal.
The hour mark brought about another decent opening for Saints as Wotherspoon drove in from the left-hand side but Hasselbaink failed to read his low cut-back as the forward dashed into the Minsk box.
But within eight minutes St Johnstone had edged themselves in front as MacLean, collecting Caddis' pass, took advantage of space in the box to shoot early on the right-hand side of the box, burying the ball under Bushma.
Some desperate defending was required in the final minutes as Minsk threw a couple of worrying crosses into the Saints box but Mannus and his back four stood strong to ensure they return home packing another impressive result.