But, ahead of Saturday's clash with leaders Arsenal at the Emirates Stadium, O'Neill has admitted he must address the situation at the end of the season with several new signings.
The former Celtic boss said: "I know people are talking about us possibly going into Europe and there is a group of sides with nothing between us at the moment.
"It's getting to a stage where my expectations are pretty high. I want them to be high but we've got to live up to them.
"Liverpool have got the strong advantage (for the final Champions League berth) because, to be honest, they have the best and strongest squad of the sides competing and you would say Everton are the next best.
"We've been amazing in the sense that we don't have a big squad and we wouldn't have been able to cope with a lot of things such as more games and injuries.
"The injuries might still happen to us but I wouldn't want to be having that small squad for another season.
"We tried to strengthen in January and it didn't materialise but that's something I'll address in the summer if we can."