Wright returned to McDiarmid Park after missing the last two games following gallbladder surgery, and he watched from the directors' box as assistant Callum Davidson and first-team coach Alex Cleland directed the team from the dugout.
Wright, sat beside the calming influence of chairman Steve Brown, admitted conceding a late equaliser was "not easy to take", but he was happy to have cemented a place in the top six.
"It's a wee bit more relaxing now that we've got top-six now, probably. That helps," he said. "I've been under strict orders as well not to get too excited, and I tried not to.
"I had the chairman beside me so he kept me nice and calm. When you've no choice, it's not difficult. You just have to deal with it.
"I have total trust in Callum and Alex, and all the staff, because we work closely together, otherwise they wouldn't be there - so, I knew the place was in good hands.
"They were on the phone regularly and Callum and Alex were popping in to see me as well.
"I was fully aware of what was going on, what was happening. Callum and Alex are two people I would trust with my life, and they have done a tremendous job when I've been away."
Stevie May's 23rd goal of the season looked to have given Wright's side all three points until Kris Doolan struck an equaliser in the final minute.
Wright, who indicated he is likely to stay out of the dugout for next week's trip to Kilmarnock, added: "I'm disappointed to draw the game in the end.
"We had almost seen it out, we were right at the death, and they got a wee bit of fortune; it ricocheted to the lad and he stuck it away well.
"To lose points in the 90th minute is never easy to take.
"Saying that, over the piece, I think Partick probably deserved something out of the game, and they got their rewards for keeping going to the end, and probably deserved a point."
Jags manager Alan Archibald admitted the draw felt like a win because of the nature of the late and dramatic equaliser, and he believes it will have given his players a significant lift for their remaining six matches.
He said: "When you score a goal so late on in the game it always feels like a victory, and it was a good time to get it.
"You start to think it's not going to come, especially against a team like St Johnstone. They are in the top-six and one of the reasons for that is the way they defend; they defend really well.
"So, we're delighted to get the goal and we kept on going. That will make a massive difference to the lads.
"There were games earlier on in the season where they played like that and didn't get any rewards.
"Since the turn of the year we've probably been getting more rewards and it all bodes well for this run-in.
"Since probably January there's been a big upturn in their belief and their confidence. They keep going, they've got a never-say-die attitude and we'll need that in the last six games."