The Black Cats face the Gunners in the Barclays Premier League at the Stadium of Light on Saturday in what will represent a dress rehearsal for their first fifth round tie in eight years seven days later.
O'Neill's men booked their place in the last 16 with a hard-fought 2-1 replay victory over Middlesbrough at the Riverside Stadium, but needed extra-time to see off the battling npower Championship side.
Just how much that will have taken out of his players ahead of their first meeting with Arsene Wenger's men, who put seven goals past Blackburn at the weekend, remains to be seen, but the Ulsterman is refusing to look any further ahead.
He said: "Arsenal will be pretty pleased that we have gone into extra-time. We will try to get ourselves ready for that game.
"The cup game will take care of itself the week after."
Sunderland had Stephane Sessegnon to thank for their victory after he spared them a nail-biting penalty shoot-out with a winner eight minutes from the end of extra-time.
Boro perhaps enjoyed the better of the first half, but found themselves trailing three minutes from the end of it when Jack Colback ran on to Fraizer Campbell's knockdown and smashed home a left foot shot off the underside of the bar.
Phil Bardsley made a superb block to deny Tony McMahon a quickfire equaliser, but the Teessiders dragged themselves back into the game 12 minutes after the break when January signing Lukas Jutkiewicz fired home his first goal for the club.
However, despite a rousing finale, there was no splitting the teams and as Boro rallied again in extra-time, it was they who looked the more likely victors until Sessegnon struck.
O'Neill said: "The penalty-kicks were a concern because it's a lottery. I obviously thought it was going to go that distance because the two teams were tiring.
"I know they were pressing as the ball broke down, but I am pleased from a selfish viewpoint that it didn't go to penalties.
"I thought the game was going to be hard, and it was. Over the two legs, I haven't been surprised - but I am going to stick up for us, I thought we were the better side today [Wednesday]."
Boro counterpart Tony Mowbray was able to take little consolation from the fact that his promotion-chasers had pushed a Premier League side all the way.
He said: "The overriding emotion is disappointment, of course. It's a game we haven't won and somewhere along the line, statistics will be used to say we haven't won since Boxing Day, as I am hearing a lot at the moment.
"It's little consolation. The bottom line is when you go to extra-time, you have got to come out winning the football match, not having any consolation that you might have done okay in the game.
"We didn't win it and Sunderland found a way to win it tonight [Wednesday]."
Once the dust settles, he may be able to take some positives, one of them certainly being the emergence of 19-year-old striker Curtis Main, who made an impressive full debut.
Mowbray said: "The bottom line is if he wasn't ready to play, he wouldn't have played.
"I don't think we should sit here and belittle the boy. He's on the pitch because in my mind, he has done well enough in the development squad and he deserves an opportunity.
"Because of injury situation, his opportunity was tonight [Wednesday], and he did okay, he didn't do himself any harm."