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 told BBC Radio Scotland: "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."
- Sports & Recreation
- BBC Radio Scotland