Gerrard said: "The effort was there but the result wasn't. That's what was important. We're obviously hugely disappointed.
"The first goal was a big blow. Our idea was to start really quick and get a goal up and let them know they were in for a game - but we found ourselves 2-0 down and with a mountain to climb.
"The second half was a big improvement but when we got back into it we should have shut up shop. Instead we went for that third goal and they hit us on the break.
"You've got to learn from that. When you get back into it you've got to see it out and take a draw. But we took risks and got done on the counter-attack.
"We had a mountain to climb and climbed it. We got back into the game and their third goal was disappointing."
Gerrard admitted little was said by under-fire McClaren in a stunned dressing room as England failed to reach the major finals of a tournament for the first time since the 1994 World Cup.
He said: "The manager was disappointed and not much was said. He thanked us for our efforts over the last couple of years. It was a disappointed dressing room.
"It's the most disappointing day of my England career. To lose in front of 88,000 supporters when we had a great chance of going through is hard to take.
"It hasn't really sunk in just yet but it is going to hurt for a long time."
Gerrard added: "It's difficult to comment on the manager straight after a game like this. From the player's point of view we've got to take the criticism, get on with it and try and bounce back.
"There's a lot more football to play in the future and we've got to bounce back. Obviously we're disappointed at the moment but we have to try to get it out of our system. It will be difficult."