The Arsenal forward accepted that luck was not on the Three Lions' side, but insisted the future is bright for the youthful squad ahead of the World Cup qualifying campaign
The Three Lions held on for spot-kicks despite an Azzurri barrage, only for Young's effort to strike the bar and Cole's to be comfortably gathered by Gianluigi Buffon, leaving Alessandro Diamanti to seal a 4-2 shoot-out win.
"The two Ashleys are strong enough lads to come back from this and the [other] lads will be with them," the Arsenal forward told The Mirror.
"They are two of the most experienced players in that dressing room and they will bounce back from this [and be] even better players. I do not worry about that at all. From the next tournament we will be better, they will be stronger.
"I feel for every single player. It is not one of those scenarios you want to be involved in when you are on a losing side. I feel it as I am on the losing side. It is a sad way to lose.
"These are the sort of occasions you do not want anyone to be involved in. The players, the supporters, friends and family. It is a bitter, cruel way but, like I say, that is the way it goes.
"We have to learn some lessons from [Sunday] as that is important for the young players - me being one of them."
England have recorded just one shoot-out victory in eight attempts, and Walcott can offer no explanation.
"I don't know how to answer why we cannot win penalty shoot-outs," he went on. "It can go either way. It is a difficult one. Anyone can win.
"I think penalties are always down to luck. It is a lottery. It is just the way it goes in football. You can practise and practise as much as you want but when it comes to the occasion, the big stage, it is always difficult. I hate watching it when I am back at home."
Walcott concluded by looking ahead to the 2014 World Cup qualifiers, which start in September.
"We have got to look forward to the World Cup qualifiers - that is going to be tough. We need a break because we have a tough season ahead," he added.
"But we have got to look forward to the future because it is going to be bright, I am sure of that."