Arsenal won their second FA Cup in as many seasons last weekend and Winterburn has moved quickly to settle the debate over winning one domestic cup competition is enough for a club of their size.
“I always say the same thing, when you win a trophy it has to be considered a successful season – If you want to break each one down, the Champions League was very disappointing, if you look at the league they were very consistent after Christmas, but not so good before Christmas,” he said.
“Wenger knows now that his team have got to deliver for him over the next couple of seasons.”
The Premier League and the Champions League will be the two competitions that manager Arsene Wenger will covet more than anything else.
At one point last season it looked as though the Gunners could mount a late challenge to Chelsea but the Blues pulled away and put distance between themselves and their rivals.
The Champions League is a competition that Arsenal have consistently qualified for under Wenger, but they have always found it difficult to get past the last 16 stage of the competition.
One way Wenger can improve his team’s chances of winning both is by continuing to invest heavily in his playing staff.
He has the mentality of not improving the squad unless he feels the opportunity is there to add quality, but Arsenal need to respond because their rivals are all likely to make moves and spend tens of millions.