The 32-year-old has impressed for the Toffees since signing a season-long deal on transfer deadline day.
Barry believes that the supporters at Goodison Park are more appreciative of the role that he plays in midfield than elsewhere.
"Everybody has welcomed me in and the manager has suited my style, so I think that played a big part in me fitting straight in," he told the club's official website. "Obviously positive results help as well.
"The job I do is an unspectacular one so maybe the Everton fans have the ability to look at the game a bit differently to fans at other clubs and appreciate what I do."
Barry has made four appearances in all competitions for Everton so far this season.