A goalless draw against Costa Rica on Tuesday afternoon signalled the end of England's campaign in Brazil, following defeats against Italy and Uruguay in their opening two Group D games.
Despite the disappointing showing, Lampard was quick to praise his side's "immense" supporters and highlight the positives from the whole experience.
"From in and around the hotel after we came out here, they followed us and we had it in a good way," the 36-year-old is quoted as saying by FIFA.com. "This morning before and after they were immense. It makes you feel a bit bad we have not given them a longer stay. I am very proud to have a following like that.
"[The young players] see that they back the manager and were singing for him. They can see the squad is young and the young players will benefit from this bad experience. Let's not forget we have been knocked out very early but if the fans stick with the younger players and encourage them, they will help the players."
Lampard also revealed that he has yet to make a decision on his own international future.