Villa's win at Portsmouth on Sunday re-ignited their hopes of finishing fourth and securing a lucrative place in among Europe's elite.
But O'Neill knows it will be tough to win the battle for a top-four finish as they have a testing run-in and even a place in the Europa League is far from assured.
Wednesday night's Premier League hosts Hull will be fighting for their lives, while Villa entertain arch rivals Birmingham before tackling Manchester City who have their own Champions League aspirations.
Villa's final game of the season is at home against Blackburn and O'Neill said: "There are no easy games.
"We are playing catch-up, we know that and have been doing that for a few weeks and the situation is really straightforward.
"It is that we cannot afford to slip and we have to win our games.
"Even then, if we win all our games it is not entirely in our own hands.
"But the other run-ins that the other teams have are particularly difficult. I think everyone's is difficult and we have just got to keep going.
"That is why winning so late on at Portsmouth last weekend was important to us and that is the attitude that we will take into the game.
"In fairness, that is the attitude we have taken into the last few months even though we might have not had the wins that perhaps our play deserved."
With Hull battling for their Premier League survival, the stakes are high for both sides.
Iain Dowie was brought in by Hull to try and guide them to safety and O'Neill knows what a tough task he faces.
"It is difficult," added O'Neill.
"I think it is too easy for people to say you just need a change of manager and everything will be all right.
"It is just not as simple as that at all.
You have to get to know players and I think that given the number of games you have to try and turn things around it is not that easy.
"Hull made the change and they brought him in and he is doing his utmost to keep them in the league.
"While there might be a cagey opening to the game against them I can't see the game developing along those lines at all because both sides have really got to go for it."
Villa, who will leapfrog Liverpool into sixth with a victory at Hull, will not allow themselves to be distracted by the plight of Dowie's team as their sole focus is on taking 12 points from their final four games.
"Where there is life there is hope," said O'Neill.
"Anything can happen in the last four games.
To give ourselves a chance we have to win every single game.
"Of course, you need a little luck here and there.
We will keep battling and while the chance is there we are going for it.
"It is really vital that we win the games to give ourselves a chance of European football in any description."
O'Neill also backed midfielder Fabian Delph to bounce back strongly after he was ruled out for up to eight months with a knee ligament injury.
England Under-21 international Delph was injured in training last Saturday when he ruptured the anterior cruciate ligaments in his left knee.
He will have to undergo reconstructive surgery and manager Martin O'Neill said: "He puts his heart and soul into training.
"He loves the football and he just turned away from a couple of players, someone came in to close him down and he has fallen awkwardly.
"He will recover from it.
These things were career threatening about a quarter of a century ago but nowadays players recover from them very well and just take it as a normal injury, albeit one that takes longer to recover from."