Gerrard was unable to prevent his side from crashing out in the group stage without claiming a victory, but Beckham believes that the Liverpool midfielder is still the right man to set an example for the younger players ahead of the Euro 2016 qualifying matches.
"I think it would be great if Steven continues because it was a disappointing tournament for the whole team and the captain kind of takes the real kind of brunt of things," the former England skipper told Sky Sports News. "But as a captain you feel a certain responsibility to lift the team.
"Stevie has done that for many years for Liverpool and for England. He has always been a real motivator, the way he plays and his passion that he shows on the pitch.
"I would love to see Stevie continue because I think these young players need someone to look up to and a mentor - someone that has been there and done it - and I think that Steve is a great captain. He has been for Liverpool and England."
England return to action in a friendly against Norway at Wembley on September 3.