England were beaten 4-2 on spot-kicks after their quarter-final clash in Kiev had finished goalless after extra-time.
This was the latest in a long line of penalty shoot-out exits from major tournaments, following on from 1990, 1996, 1998, 2004 and 2006, and while Gerrard praised his team-mates for their showing in Poland and Ukraine, he conceded it was a painful way to go out.
"Everyone's been great in training, every time we've come out I think we've done the country proud, but again we're going home with heartbreak, which is difficult to take," he told BBC1.
The Liverpool midfielder added "I just feel for the players who from day one have given everything and today [Sunday] we did the same.
"This time in the penalty shoot-out we thought we might have the bit of luck we needed but it wasn't to be.
"Credit to Italy they are fantastic team and they got the luck in the shoot out."
England found themselves in the ascendancy in the shoot-out when Riccardo Montolivo missed Italy's second kick and Wayne Rooney scored the next to put Hodgson's men 2-1 up.
However, Italy slotted home their next three kicks while Ashley Young's effort come back off the crossbar and then Ashley Cole saw his attempt saved by Gianluigi Buffon.
Theo Walcott is confident Young and Cole will recover from their penalty agony.
He said: "I feel for every single player in a shoot-out. It is not one of those scenarios you want to be involved in when you are on a losing side.
"But the two Ashleys are strong enough lads to come back from this and the lads will be with them.
"They are two of the most experienced players in that dressing room and they will bounce back from this even better players. I do not worry about that at all.
"For the next tournament we will be better, and they will be stronger."
Walcott added: "I think penalties is always down to luck. It is a lottery. It is just the way it goes in football.
"You can practice and practice as much as you want but, when it comes to the occasion, the big stage, it is always difficult."
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England goalkeeper Joe Hart admitted he felt "terrible" after being knocked out of the competition
He said on Radio Five Live: "We've gone out of a tournament that we've laid the foundations for really well, played with everything we've got and unfortunately we weren't good enough tonight, losing on penalties."
England rode their luck on occasion during the match with Italy, twice hitting the woodwork as well as creating a number of other decent chances.
The Azzurri also thought they had won the match six minutes from time only to see Antonio Nocerino's header correctly ruled out for offside.
Asked if he thought it was going to be England's night after those escapes, Hart said: "I thought it was going to be our night whether those things didn't happen.
"I thought it was going to be our night because of the side we had, the heart we had, the quality we had, but unfortunately it wasn't to be, we didn't do well in the shoot-out, myself included."
The Manchester City custodian also admitted he was struggling to take many positives from the experience immediately after the match.
"I'd like to be optimistic now but that's not the feeling in my heart at the moment," he said. "I'm an emotional guy and I put everything I had into these past couple of weeks.
"I'm gutted for the people who paid money to come out here to support us and see us and for the people back home."
On how he will reflect back on the tournament overall, Hart added: "Right now, not well. We'll have to wait and see in a couple of days."
Hart may have been struggling for positives but Hodgson was optimistic about the future.
He said: "If this group of players continues to show the same degree of determination and the will to be a team, and to work hard as a team, we've got quality players to come into our squad who will obviously to add to the competition...I'm convinced it won't be that long before we beat a top nation in a competition.
"We had our chance today and we came close to taking it but not quite, but I think we've just got to keep building on what we've done in this tournament.
"We've got to make certain the good things that we've done remain and we've got to keep working on the aspects of our play where we could be a little bit better."