Seeing his side score two goals in the last six minutes to salvage a point would normally have a manager punching the air in celebration but Mick McCarthy's joy was laced with an anger that left him tempted to strike out in an altogether different way. "I'm up for a scrap," he told journalists at the post-match press conference. "As a matter of fact, if any of you want a scrap right now I'd be more than happy to accommodate you."

In truth, the target of McCarthy's ire was not journalists but the vociferous, and numerous, members of the Molineux crowd who chanted for him to be sacked as Wolves were 2-0 down to Swansea City and being utterly outplayed, seemingly on they way to a sixth straight league defeat. The goals had been scored by Danny Graham and Joe Allen in the first half and until deep into the second period the visitors were so dominant that there seemed no possibility of Wolves salvaging even pride, let alone a point.

The home fans had been booing since early in the game and became particularly furious in the 68th minute, when McCarthy made two unpopular substitutions, withdrawing the wingers Matt Jarvis and Adam Hammill and replacing them with Adlène Guedioura and Stephen Hunt. "I thought the substitutions were rubbish, I can't explain the comeback," a snarling McCarthy said sarcastically. "We were just very, very lucky." There was no mistaking the irritation, even the sadness, from the man who took charge five years ago when Wolves were in the Championship and now seems to feel betrayed by the seeming lack of faith in his ability to prevent them from returning there.

Although he hinted at vindication, McCarthy was certainly not so bold as to claim that his side had played well. They lacked ideas, confidence and, most of all, the ball, which was almost permanently at the foot of a Swansea player. Tactically and technically, the visitors, despite having lost their previous four away matches this season, were superior and Wolves could barely get close enough to tackle.

The home team did have chances in the first period –Karl Henry's long shot in the second minute forced a good save from Michel Vorm, who also had to make a reflex block from a Jamie O'Hara effort in the 20th – but Swansea were worthy of the two-goal lead that they took into the break. Graham scored the first in the 23rd minute, finishing from close range after Mark Gower had clipped a perfect pass to him from deep. Graham created the second with a run from midfield that went undetected by everyone except Angel Rangel, who chipped the ball from the right-back position into the striker's path. Graham's low cross from the right was turned into the net by Allen.

In the programme McCarthy and his chief executive, Jez Moxey, had pleaded with the fans to be patient, arguing that their recent run had been more down to bad luck and bad refereeing decisions than bad play. No such case could be made here, as by comparison to Swansea Wolves looked second-rate.

On three occasions in the second half Scott Sinclair could have extended the visitors' lead but was denied by the goalkeeper Wayne Hennessey. Wolves were hanging on by a thread, and McCarthy's position also looked highly precarious.

Salvation, if that is what it was, came suddenly. Swansea failed to clear a corner in the 84th minute and Sam Vokes was allowed to shoot from eight yards. Vorm saved but Doyle swept in the rebound. Two minutes later Wolves drew level. Doyle raided down the left and then pulled a low pass back to O'Hara, who blasted into the net to secure an improbable point.

"We've played better than that over the last five games but not got anything," McCarthy said. "We needed something from this game and we got it. If that's a turning point, then brilliant."