Fifa are currently trialing two separate systems, Hawkeye and GoalRef, and are said to be considering introducing one or the other for this year's Club World Cup
The demand for goal-line technology has intensified this season, particularly in the wake of a controversial goal awarded to Juan Mata in Chelsea's FA Cup semi-final win over Tottenham Hotspur at Wembley last month.
Barry, for his part, feels that some decisions should remain the sole responsibility of the man in the middle. However, after getting a first-hand look at 'Hawkeye' - one of the two goal-line technologies currently being evaluated by Fifa - during a testing session at St. Mary's on Thursday, he believes it would be a wonderful aid for officials.
"Nobody likes to see games decided on decisions of controversy," the referees chief commented.
"Whether it's penalty or not, or whether someone is sent off or not, are matters of opinion for the referee.
"But this is actually a matter of fact: whether the ball has crossed the line or not.
"So, if we can get to a situation where we have the technology and it's successful so we can that one decision absolutely right, whether the ball has crossed the line or not, I think that'd be a major step forward."
Meanwhile, Steve Carter, managing director of Hawkeye, revealed that his company's product is effectively fool-proof and would avoid the kind of debate which followed Andy Carroll's 'goal' against Chelsea in the FA Cup final.
"The way the system works is that we have seven cameras at either end and they're special high-speed cameras," he explained.
"And when the ball travels through those fixed cameras, our software automatically finds the ball because you've got more than one camera that can see the ball at any one time, so you can accurately calculate its three-dimensional position."
Hawkeye is currently competing with 'GoalRef' for Fifa's endorsement.