Villa have little time to feel sorry for themselves after the 3-0 Wembley semi-final defeat against Chelsea as they entertain Everton in a Premier League encounter on Wednesday.
Striker Carew is adamant the Villa players remain motivated even though they are now eight points adrift of fourth-placed Manchester City.
But in terms of the bigger picture the Norway international knows how important O'Neill will be to Villa.
He said: "Will Martin O'Neill stay? I haven't really thought about it and I don't think the manager wants us to think about it either.
"I think he wants us to focus on the games.
"The speculation will be in the media but we have to go out there and perform and, in his mind, he is thinking about the game as well when we go out there.
"Is it important that Martin O'Neill stays? Absolutely. You see what he has done for the club. It is very important for Villa that he stays."
Carew added: "We are still motivated and fourth place is still in range for us. We are really up for it and will be ready for it again on Wednesday.
"It is always important for everyone to get results and you want to perform and everyone has got big ambitions at Villa.
"You have seen that in the last year. We will be looking to improve every year. It is important as well for the other teams. They feel it is important as well to get that fourth place.
"We will do everything to try and get it. We haven't given up. We are a few points behind Tottenham and Manchester City but that can change in almost an instant, in a couple of games.
"We also know Tottenham have a hard run-in. We just have to go for it."
Carew believes it will benefit Villa if they improve their squad.
He said: "I don't want to comment on whether we should or not bring in more players - but the more better players you have, the better you are as a squad and as a team, and also with it being a long season.
"In the club, we always welcome good players, the more the better."
Carew also made it clear he would be happy to extend his stay at Villa Park.
He said: "I have a year left after this. I am really happy at Villa. Do I want to stay long term? Yes, I really enjoy it at Villa.
"It is fantastic being at Villa but I am not commenting any more on new contracts or new players."