Barry, who is spending the season on loan at Goodison Park from Manchester City, played a crucial role in the victory, preventing a goal as he blocked a shot from Samuel Eto'o that appeared destined for an unguarded net.
And, after Steven Naismith's header proved to be enough to give Roberto Martinez his first league win as Everton boss, Barry revealed his happiness with his display and that of his team-mates.
"It could not have started better for me," he told the Liverpool Daily Post. "Three points was what it was all about and to get that against a team like Chelsea has set us up and will give us a lot of confidence for future games.
"On a personal note a good performance is also something to build on."
Barry left a Manchester City side who will compete in the UEFA Champions League this season in order to join Everton, but the England international is keen to help his new club reach Europe.
"That (missing out on the Champions League) won't matter to me now because my focus is purely on Everton and I'm not worried what's going on," he added.
"I'll be enjoying this win and then starting the preparation for next week and looking forward to that. That's the aim.
"Getting into Europe with Everton is one of the targets and the longer the season goes on the more we'll set ourselves more targets."
