The pair chose last season to hang up the boots.
"Some players would say it makes them feel old but, mostly, it just makes me feel proud to have been part of a generation like that," said Beckham.
"These players have all been world class for many years. It's sad because they have been amazing servants for United and England.
"Scholes is the one player they want to replace. He is such a great talent and he will be missed. They're going to have to get someone special."