The former England international made his debut in a 1-0 win over Chelsea on Saturday after being loaned out as a result of losing his place in Manuel Pellegrini's plans.
Asked about missing out on the first midweek of Champions League group games, Barry told reporters: "That won't matter to me now because my focus is purely on Everton and I'm not worried what's going on.
"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.
|13/1||Everton are 13/1 with BetVictor to beat West Ham 2-0
"It could not have started better for me," the midfielder added of his debut. "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 also commended his 19-year-old team-mate, Ross Barkley, who made his England debut earlier in September against Moldova.
"I had two days training with Ross. He has bags of confidence and lots of ability," he observed. "If he manages to keep a level head and keep learning, he can go all the way. The sky is the limit for him.
"It's surprising how strong the squad is and, when everyone is fit and available, the competition here will be really good, which is what we need."