O'Neill said: "Adam hasn't been picked for England because Roy Hodgson probably thought his performances for us haven't been consistent enough.
"For the most part as a team we've not been great, and at the moment Roy has other players to choose from. Does that mean Adam's international career is finished? Absolutely not.
"I think he'll have gained a greater appreciation of things this season and we know he's still a match-winner on his day.
"He has to show a consistency here. He's stepped in and fans might have felt he was going to win games single-handedly for us and that all would be rosy but I'm sorry it doesn't work like that. He needs to add a bit of consistency to his game."