Barry played a key role as Everton won at Old Trafford for the first time in 21 years last season, triumphing 1-0.
The 33-year-old midfielder also tasted success at the stadium during his time with Manchester City, featuring in the 6-1 mauling in October 2011 en route to the Premier League title.
Barry was also part of the City team that beat United 2-1 in April last year.
And speaking ahead of Sunday's clash, Barry believes Old Trafford is not as daunting as it once was for visiting teams.
"I think it has [lost its fear factor]," Barry said. "It took me probably 12 or 13 years to win a Premier League game there.
"But I think I have won the last three times there, it's just my experience but it sort of shows you maybe it's not what it once was.
"At the same time we need to show them the respect they deserve. They have got loads of talent, and if they put it together on the day they can probably beat anybody so it's down to us to produce a good performance."
Everton left Old Trafford with all three points last season thanks to Bryan Oviedo, who struck four minutes from time as the Merseyside club won at the venue for the first time since August 1992.
Barry said his team-mates will be hoping to repeat that feat this weekend.
"It was fantastic to win there last season and a significant result," Barry said.
"That was a big focal point last season for the confidence of the club to come away from there with three points. And I am sure we will be looking back at that result and [trying to] do it again."
