The Gunners host Aston Villa in the fourth round on Sunday looking to lift morale following a third straight league defeat when they lost 2-1 at home to Manchester United last weekend, which saw them fall five points behind Chelsea.
Wenger, 62, has won the famous old trophy no fewer than four times since taking charge in 1996. The last came seven years ago, and there has been no silverware since.
The Arsenal manager, however, insists he would not take cup glory at Wembley in May ahead of securing another campaign in the Champions League.
"I have always told you exactly the same, the priority is be in the top four," said Wenger.
"In recent years I felt that we produced always the consistency at the top, top level and it is not enough for some people maybe, but for me that is the brand of a top level club - consistency in the top four."
Wenger continued: "I love the FA Cup, I think it is a top-level competition and I will always fight to win it.
"I won it four times and lost one final, and I don't know how many semi-finals. I always try to win every single competition.
"If you look at my record you will see the FA Cup is important for me. I think our record is better than all of them over the past 15 years.
"Even last year we went for four trophies. How many teams go for four trophies this season? Nobody.
"We always try to go for everything and for a long, long time last year we went for trophies late in the season, and still we will try to do the same and try to win the FA Cup."
Arsenal have some of their defenders closing in on a return to fitness, with full-back Bacary Sagna - out since the defeat at Tottenham in October because of a broken fibula - having an outside chance of being included in the squad.
However, midfielder Jack Wilshere has suffered a setback in his planned return from ankle surgery.
Despite a packed treatment room, Wenger insists the answer is not just to go out and spend money.
"We played recently with 10 players out, to have only two or three out would help us a lot, much more than the transfer market," he said.
"You can look around at all the big clubs and who bought players? Nobody because you can't find players at the moment who can strengthen big clubs."
Alex McLeish believes Aston Villa should approach the tie with "no fear" even though he concedes Wenger's side will be favourites to reach the fifth round.
The Villa boss feels the Gunners will be the team under pressure and their players aware of the need to halt their recent poor run of results.
McLeish also has the memory of triumphing over Arsenal in last season's Carling Cup final when Birmingham boss while Villa won 2-1 when they visited the Emirates Stadium last season.
But the Scot knows Villa will have to be at their best if they are to spring a surprise result despite Arsenal's current lengthy injury list.
McLeish said: "I don't see why we should be fearing Arsenal. I am sure the lads will remember what they have done at the Emirates before.
"Statistics don't determine the outcome of this latest encounter but it does offer the players evidence they can do it against the best of the Arsenal teams.
"There is a good bit of confidence going into this next game. It's the FA Cup, we are away, the pressure will be more on the home team Arsenal to win.
"I'm sure they are under pressure with the fact they've lost two or three games. You rarely see the top clubs losing four in a row.
"But at the same time we are not going to be shouting from the rooftops `we're going to do this, we're going to do that.'
"We have to be at our best defensively because they have some great attackers - but we have attackers ourselves who can also hurt people."
McLeish intends to field his strongest available side against Arsenal even though they have a home league game with QPR to contend with before a visit to Newcastle next weekend.
He said: "The magic of the FA Cup dictates you can't leave anything to chance and you have to go and do your utmost to get through to the next round."
Strikers Gabriel Agbonlahor (illness) and Emile Heskey (Achilles) plus midfielder Stephen Ireland (hamstring) are all available.
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Arsenal V Aston Villa - view commentary, squad, and statictics of the game live.
Arsenal V Aston Villa - view commentary, squad, and statictics of the game live.
Source: PA
