The Villa boss will field a weakened side in the Uefa Cup last 32 second leg clash with CSKA Moscow on Thursday.
Only three players - Luke Young, Curtis Davies and Zat Knight - have been included in the squad from those who started in the 1-0 Premier League defeat to Chelsea on Saturday.
The Villa boss has wielded the axe as he seeks to guide his side into next season's UEFA Champions League, as his team have two league matches to follow in quick succession against Stoke and Manchester City after the CSKA game.
Speaking prior to O'Neill making his decision, Barry, who was one of the players to be dropped, said: "It's always a difficult one, especially for the manager.
Priority"If you're looking at the game with Stoke on Sunday as the priority then it might be vital a few players do get a rest.
"Last Wednesday's game (with CSKA) maybe caught up with us because we had a tough game against Chelsea (Saturday's 1-0 defeat)."
Winger James Milner has also been rested but he still believes Villa can progress against CSKA, whom they drew 1-1 with in the first leg at Villa Park.
"It's obviously the manager's decision," said Milner.
Good enough"Whatever team we put out, it will be good enough to get a result because we've a squad of quality players, even if it might not be the biggest.
"We know they (CSKA) are a good team, but we've a lot of good players as well, not just the 11 that played against Chelsea."
Milner hopes Villa can progress, adding: "It's a massive competition, and a club like Villa wants to be in Europe. There is no point being in Europe if you don't want the games.
"We know they're coming up thick and fast, but that's what happens when you are a successful team, you're going to be playing every few days.
"You would rather do that than be playing once a week, be in mid-table, out of all the cups and having plenty of days off.
"I know where I'd rather be. It's tough on the squad sometimes in having to recover, and with injuries, but that is what playing at the top is all about."