Gerrard, who won 114 caps for his country, said: "There is a frustration when I look back on my England career.
"I look at some of those penalty shoot-outs we lost and see how close we got to progressing to certain semi-finals - and then from there you never know what would have happened.
"I have got no excuses because the stage was there to go and do it. But unfortunately we just fell a bit short.
"I certainly don't regret playing for England or turning up and giving it a go because I loved every minute of it. But there is a sense of frustration - we had opportunities to do much better."