Gerrard ended his 14-year association with the England side on Monday afternoon when he officially announced his decision to retire from international football.
The Liverpool skipper finishes his time with the Three Lions as the third most-capped player of all time with 114 caps, just one behind Beckham, who is the most decorated outfield player.
The former midfielder also stated his belief that the Anfield star was even better than United greats Beckham and Scholes.
He said: “For me, he’s been the best midfield player that England have produced in the last 20 years.
“I think I would include Paul Scholes and David Beckham in that. I think he surpasses them.
"In terms of talent and having played with him, and I’ve watched him for many years now, he is one of the best players I’ve seen.
“The difficulty now is how do you feel that void? Who will be the next England captain?”
Speaking of his decision on Monday, Gerrard explained that Liverpool's return to Champions League football for the first time in five years next term was a big factor behind his decision to step down from his role with Roy Hodgson's side.
He told the Football Association's official website: "I do feel as though I can still play for England in September, but big-picture wise over the next two or three years, the best thing for my body is to step aside out of the international fold and give my body the best chance to perform well.
"I have to look after my body and ensure that I can keep playing to a high level for Liverpool. I believe this is the right decision, and having Champions League football back at Anfield is another big factor in my decision.”