In seven years in the job, many of those in trying circumstances, Mark Robins has guided Coventry to two promotions, the Football League Trophy and, last season, to within a Wembley penalty shootout of the Premier League. This, however, was arguably his greatest feat yet, leading Coventry into the FA Cup semi-finals for the first time since the club won the competition in 1987. No wonder some supporters consider his work worthy of a statue. Now they are heading back to the national stadium, after defeating Wolves in a tantalising tie, decided in the 100th minute by a magnificent, unerring finish by Haji Wright.

But then Robins, so often serenity personified in the eye of a storm, allowed the occasion to get the better of him, running to celebrate wildly in the face of a 13-year-old Wolves ballboy to the left of the away dugout. Gary O’Neil, the Wolves manager, waited to confront Robins about his “disgusting” behaviour, an unedifying episode that tarnished the most joyous moment. Robins had been irked when the teenager smirked after dropping the ball to delay a restart moments before Wright’s intuitive brilliance clinched a spot in the final four.

Robins brought up the incident, which happened out of view of the television cameras, in his press conference and issued a public apology. “It really annoyed me, but he’s a kid and at the end of the day I’ve reacted,” the Coventry manager said. “We’ve scored the goal and I’ve gone and celebrated in front of him. I do not show emotion very often but I did today – that’s what the FA Cup does to you. I apologise unreservedly to him.”

Two goals in the final seven minutes of normal time flipped this game on its head, Wolves starting the minimum of nine minutes of stoppage time with an unlikely lead courtesy of strikes from Rayan Aït-Nouri and Hugo Bueno. Ellis Simms, who scored Coventry’s first goal, equalised in the 97th minute then helped tee up Wright’s superb, curled winner. Wright used the Wolves captain, Max Kilman, as a mannequin and caressed a first-time shot into the bottom corner after the substitute Callum O’Hare dug out a cross from the left flank for Simms to lay off. Coventry’s players could not mob Wright quickly enough. Kasey Palmer, replaced by O’Hare, sprinted 40 yards from the bench, knee-sliding on the turf before joining the party. Wolves were floored.

Robins has transformed a dysfunctional club, rebuilding them from the bottom up and restoring Coventry’s proud name, and few could begrudge the celebrations at the final whistle. He has steered them through incessantly choppy waters, making light of ground shares, skeleton staff and unplayable pitches, and here he was able to drink in the reality of it all. “It has come from a really dark place across a 10-year period, to a point where it is being taken seriously again,” he said. “The fact we’re in the semi‑final of the Cup, you need to pinch me a little bit.”

Robins famously scored a crucial goal for Manchester United en route to winning this competition in 1990. The first strike here was a contentious one, so much so that it took four minutes for the video assistant referee, Graham Scott, to award it, after the ball bobbled in off Simms’s right arm. Liam Kitching headed a Palmer free-kick across goal, Joel Latibeaudiere got a touch and then the ball struck Simms, who missed a sitter in the first half, and bounced into the net. Even the Wolves supporters jeered as Stockley Park stewed over the decision. Robins, then more in character, was unmoved.

Wolves were light in attack, with the 19-year-old Nathan Fraser, who was close to joining third-tier Shrewsbury on loan in January, again tasked with leading the line in the absence of the injured Matheus Cunha, Hwang Hee-chan and Pedro Neto, who may not return before the end of the season. So it was down to Aït-Nouri to inspire Wolves, volleying in an equaliser before teeing up Bueno with a clever pass. “The result is the accumulation of where the club has got to in the last couple of years,” O’Neil, who had moved Mario Lemina forward from midfield to join Pablo Sarabia in attack, said, pointedly. “We find ourselves with only one fit senior attacking player … at a Premier League club.”

Wolves presumably thought Bueno’s strike would clinch victory but Coventry ensured a barmy finish. After Sunday’s semi-final draw Robins will turn his attention to plotting the downfall of perhaps another Premier League side at the stadium where things ended in tears last May. “We get to go back and [I get to] remind myself who the potential opponents can be – that can put the fear of God into you, but we’ll leave that for another time,” he said, smiling.