Saints have lost their last two league games, a 1-0 loss against Inverness and then a rare home defeat against Aberdeen.
And they travel to Firhill looking to double their tally of away wins for the season.
Wright, whose side sit sixth in the table, said: "I think the last two league games we probably haven't played as well as we can.
"We probably haven't done enough to deserve to win the games against Inverness and Aberdeen, but I also think we didn't do that badly that we deserved to lose them.
"We have made mistakes at key times in the games, particularly at Inverness going behind early, it was a poor goal to concede from our point of view.
"Aberdeen, even though it was a great strike from Peter Pawlett, we have got to look at how we could have done better and we gifted them the first goal by giving away possession so cheaply.
"With a bit more concentration and better play, we could maybe have had two 0-0 draws against two very good sides."
Thistle have not won a Scottish Premiership game at home but they ended a five-match losing streak with a point at Hibernian last weekend and Wright knows they will pose a threat.
"They have done really well," the former Northern Ireland goalkeeper said. "They haven't surprised me because I watched them a lot last year and they have some very good players and play a good style of football.
"Their home record probably isn't what they would want it to be, but we can't look at that, it's a totally new game and we have got to make sure we start improving our away record.
"We have got to be better on the road. For some reason we haven't been too good, our set-up is not much different from what we have at home. That's one aspect that we are hoping to improve."