After a goalless 120 minutes, Roy Hodgson's men eventually succumbed in a penalty shoot-out, with former West Ham forward Alessandro Diamanti scoring the winning kick.
Speaking to BBC Sport after the game, the England captain admitted he was hoping the Three Lions might have been able to reverse their poor record in penalty shoot-outs but admitted it simply was not their night.
"The players have given everything. I thought we might have the luck in the penalty shoot-out but it wasn't to be," said the midfielder. "When you get your nose in front during a shoot-out, you just hope you can hang on but credit to Italy, they got the luck in the shoot-out.
"The lads at the back were fantastic; we have done the country proud but we go home heartbroken and that is hard to take."
Striker Wayne Rooney, who scored in the shoot-out, also admitted he had no idea why his country seemed to perform so poorly when it came to spot-kicks.
"We're gutted about it, people weren't expecting much this tournament but we've shown we are a good team," he added. "I don't know why we can't win penalty shoot-outs, it's a hard way to go out and it's happened too many times now."
Theo Walcott, meanwhile, felt his side had performed well at the tournament but admitted he was already looking forward to the World Cup qualifiers.
"It just wasn't mean to be and it's a cruel way to go out. The lads can be proud that we got this far," he said.
"Bring on the World Cup qualifiers now. We'll be much stronger next year. We couldn't get the goal at the start and Buffon made some world-class saves. We've had some luck, at times, but tonight, it didn't go our way."
Goalkeeper Joe Hart also added his thoughts and refused to be downbeat despite exiting the tournament and failing to save any of the Italian penalties in the shoot-out.
"I face penalties against Mario Balotelli on the training ground and I felt confident, but he took a good penalty," said the Manchester City man.
"I'll take away the great way we qualified, we've lost at the end of the day, but I don't think anyone has let the country down and we have adapted well to the manager."