The former Premier League referee is part of the International Football Association Board (IFAB) sub-committee charged with deciding whether current systems are ready to be implemented in the sport.
British company Hawk-Eye and German-Danish firm GoalRef are vying to be approved as authorised suppliers of goal-line technology and were chosen for the next testing phase by the IFAB.
Barry was at the beginning of second-phase testing on Hawk-Eye's system on Wednesday in Southampton, where independent body Swiss Federal Laboratories for Materials Testing and Research (EMPA) undertook on-field research.
The process will continue on Thursday and next week the system will be tried in the Hampshire Senior Cup final between Eastleigh and AFC Totton, with another match to be tested as well before the IFAB decide on July 2 whether to approve the system.
"The international board first started looking at the technology in 2005," Barry, the FA's head of senior referee development, said.
"The technology has moved on greatly since then when you look at Hawk-Eye and the quality of their cameras.
"I think really there has been the attitude that we should really try to help the referees for this very, very factual decision.
"The ball is either over the line or it isn't. It is not a matter of opinion - it is a matter of fact.
"I think what we're trying to say is 'let's find a technology that works, that actually gives the referee that vital information', because in reality the most important decision in a game is whether a goal has been scored or not.
"We're trying to give the referee as much as help as we can, assuming the technology works and we can get it licensed, but we're very, very positive [it will]."
Some have voiced concerns that the introduction of goal-line systems will result in a host of other technologies being introduced to the game.
Barry, though, remains philosophical about it and, while admitting that may come later down the line, he insists the importance of goal-line technology cannot be overlooked.
"The international board have made it very, very clear that at this moment of time we're only looking at goal-line technology," he said.
"The reason we're only looking at goal-line technology is because it is a matter of fact whereas everything else is a matter of opinion.
"We may well have that debate some time in the future but currently we're just working on goal-line technology.
"Personally, I am not in favour [of looking at everything else] but that is just one person's opinion.
"We will undoubtedly have the debate in future years but the main thing for me is let's get goal-line technology in. That's the major decision."