A disappointing start to the 2012/13 campaign has seen O'Neill fall under mounting pressure, with three wins in 16 outings leaving the Black Cats just a point above the relegation zone.
A vital victory over Reading on Tuesday has offered O'Neill a bit of breathing space, and Sunderland owner Ellis Short maintains that he has full faith in the current coaching staff.
Cuellar claims O'Neill also has the backing of the dressing room, with those charged with the task of generating results on the field of the opinion that they have the right man at the helm.
He told the Sunderland Echo: "To be honest, the talk of the manager had no influence on the dressing room.
"All the time, from the manager through to the chairman, they've showed their confidence in the team.
"No-one's really said anything about it."
Victory over Reading in midweek lifted Sunderland out of the Premier League's bottom three, but Cuellar says points rather than places are of greater concern to the Black Cats at present, with the division still so tight.
He added: "We knew even when we went into the relegation zone that the league is like that at the moment. We knew that if we won one game, we'd be out of it.
"But then, on the other hand, if you lose a game, you might fall back into it. I think it's going to be like that for a few weeks.
"We don't need to get upset about where we are in the table. We just have to make sure we keep our confidence and keep getting points."