The Auld Enemy were never at their best in the quarter-final clash, with only the Italians' wastefulness in front of goal preventing them from clinching a last four berth inside regulation time.
The Liverpool captain admitted: "We leave with our heads held high but it still doesn't help the heartbreak.
"I feel for the players who, since day one when we first met up, have given absolutely everything. Last night, we did the same.
"I thought in the penalty shoot-out we might have got that bit of luck we needed but it wasn't to be.
"In a penalty shoot-out, when you get your nose in front you are praying that you see it out and that it is your turn.
"Credit to Italy, they are a fantastic team and they got a bit of luck in the shoot-out."
The match could have been over inside the 90 minutes as Cesare Prandelli's side laid siege to Joe Hart's goal but the Azzurri couldn't find the breakthrough.
Roy Hodgson's men got what they deserved from the Kiev tie, however Gerrard said he is proud of their efforts in Poland and Ukraine.
He said: "The lads at the back were fantastic last night. Everyone has been great in training and every time we have come out I think we have done the country proud.
"Again, we go home in heartbreak, which is difficult to take."