Wright stroked the Scottish champions ahead in Perth with a neat 55th-minute finish as they were held to a 1-1 draw.
The attacker, who joined in January from Premiership rivals Aberdeen, was making his first league start.
“Since Scott has come in, everything we have asked of him he has done really well,” said Gerrard.
“He is really professional, we are working hard with him on and off the pitch. He is up to speed, he looks ready now to contribute and it was a really tidy finish.
“I thought again he showed some flashes but again there are things he can work on, but so can a lot of other people on tonight’s performance. We are really pleased with Scott.”
Despite Liam Craig’s 94th-minute penalty snatching a point for St Johnstone, Rangers remain on course for an unbeaten league season and a points total of 100 for the first time in a top-flight campaign.
St Johnstone stay sixth in the table, and climb within three points of Livingston, who lost to Hibernian earlier on Wednesday.
According to the latest figures, the hosts have less than a 10th of Rangers’ player budget, but money does not account for the doggedness, diligence and sheer bloody-mindedness embodied by Callum Davidson’s side.
Gerrard has tremendous depth in his Rangers squad, and it showed. Seven players who started the Scottish Cup castling of Celtic dropped out and fit-again captain James Tavernier returned for the first time since February. Davidson, by contrast, strengthened his line-up with four front-liners returning.
St Johnstone began at a furious clip. From a cutely-worked corner, Craig steered straight at Jon McLaughlin. Guy Melamed rasped beyond the Rangers goalkeeper, but was flagged offside, then the Israeli striker nodded into McLaughlin’s arms from a dangerous position.
It was a shame to see Melamed, who has scored two goals in his past three matches and who has emerged as pivotal cog in Davidson’s machine, hobbling off injured and visibly distraught.
After this turbulent opening, Rangers began to stir, finding their rhythm and growing into the contest. Simpson ballooned a header onto the roof of the home net. Wright was sent scurrying through on goal by a wonderful, arcing Kemar Roofe pass but out galloped Zander Clark to smother at the feet of the attacker.
The duel was full-blooded, the football less than stellar, but all Rangers needed to pounce was a sliver of opportunity.
Shaun Rooney was beaten to a looping ball in midfield by Steven Davis, and off swooped Rangers. Davis cantered to the edge of the box, slipped to his left, and Wright opened his body to caress a neat shot past Clark.
Two minutes later, chaos erupted. Rooney swivelled, blasted over and hit the deck under pressure from Borna Barisic. He roared for a penalty, but referee Euan Anderson gestured for a goal kick. Then, the official seemed to change his mind, pointing to the spot.
That was gripping enough, but it got more dramatic still when Anderson jogged over to speak to his assistant, and after a brief chat, reverted to his initial decision. No penalty.
St Johnstone, undeterred, continued to push, and push hard. In the end, their resilience was rewarded. In the dying embers, Kane won a header in the Rangers box, and was caught in mid-air by Simpson.
This time, Anderson was in no doubt. Craig was equally decisive in burying his kick.
Man of the match – Stevie May
What did we learn?
The pair do it all again on Sunday with a place in the Scottish Cup semi-finals at stake.
St Johnstone’s organisation and staying power is no revelation, but living with Rangers over 90 minutes will imbue them with great confidence.
Gerrard, though, will surely bring back some of his big names for the last-eight showdown and his side will surely be more ruthless; it will take another monumental effort by Saints to pull off a seismic shock.
What they said
St Johnstone manager Callum Davidson: “Once we lost the goal we didn’t give up, we kept going and got our rewards in the end.
“It’s not often you play against Rangers and have more shots on target than they do, so that shows how well we played. We deserved at least a point and I’m really proud of the players.”
Rangers manager Steven Gerrard: “It was a penalty, we should have won the header and it was a combination of small errors.
“But I think over the course of the 90 minutes St Johnstone deserved that little bit of luck.”
Another meeting of the two at Ibrox on Sunday (18:30 BST) in the Scottish Cup quarter-finals.
- Shots on Target
Scores, Results & Fixtures
WEDNESDAY 21ST APRIL 2021
As It Stood