Wilkins, who won 84 caps for England, was speaking after Ukraine were denied a goal against England in their final group game on Tuesday.
Replays showed that the ball had crossed the line and the fifth official was in position, but the 'goal' was not spotted and the Three Lions went on to grind out a 1-0 victory that sent the co-hosts crashing out of the tournament.
"It has gone beyond a joke - there's so much at stake with these decisions," he told Yahoo. "It seems that every other sport on the planet has it [goal-line technology], and we need it."
"I think Platini's theory has been rubbished," he continued. "The thing is, the shot wasn't drilled, it was looped. The official beside the goal had a perfect view, and if he cannot see it then something has to change. I don't think the officials themselves should be vilified; humans can only do a certain amount, we all make mistakes, and we need assistance."
However, Fifa president Sepp Blatter called the need for need for goal-line technology "a necessity" in light of the incident, and that is welcome news for Wilkins.
"It's nice to see Mr Blatter step in at last, although he is saying what we have all said for a long time.
"Football is a massive industry, and there is a huge financial impact from these decisions, both for clubs and countries. What other industry would allow injustices to stand when they have the means to put things right?"
But the former Manchester United midfielder was sceptical when asked about the potential introduction of technology to examine offsides, fouls and on-pitch disciplinary action in a 'challenge' system akin to those used in cricket and tennis.
"Football is a game that needs to flow, and if you are constantly stopping play to review decisions then it becomes a bit of a nonsense," he went on. "The offside [in the build-up to the Ukraine 'goal'] was blatant and should have been picked up and dealt with. So I don't go along with challenges."
"However, when it comes to the most crucial question of all – was it a goal? – those are the decisions where we have to make absolutely sure, and the technology is such that it would only take a second or two to know whether the ball has crossed the line. There is no appreciable delay in the game, which would not be the case with a full-blown challenge system."
For more insight from Ray Wilkins and other leading managers, plus all the coverage of Euro 2012, go to yahoo.eurosport.com.