The midfield duo, as well as a host of other players, have previously been criticised for their performances in past tournaments.
However, Carragher has claimed that the more experienced members of the set-up proved their worth to the team during the qualification phase, which concluded with a 2-0 victory over Poland on Tuesday night at Wembley.
"The theory after England had beaten Poland on Tuesday was that Hodgson should get rid of Steven Gerrard, Frank Lampard and Ashley Cole, as well as one or two others, to bring in youthful faces for Brazil. It is absolute nonsense," he wrote in the Daily Mail.
"Just because they have failed to perform at previous World Cups does not mean they should be cast aside from this one. The idea Hodgson should be looking to move them on, now that the prime objective of reaching Brazil has been achieved, is ridiculous. Without the old guard, England would be staying home next summer.
"At key moments in the qualifying campaign, the older players in the team have produced. Look at Poland as the example - Wayne Rooney set the ball rolling, Gerrard settled any lingering nerves. This is a time when we should enjoy what Gerrard, Lampard, Cole and Rooney can do and respect the service they have given.
"We should also remember the quality of football they are still capable of producing. That, above all, is why theirs should be the first names Hodgson writes down. Do not doubt that the older players remain his first choices. Gerrard is his captain. Lampard was picked ahead of Jack Wilshere, while I'm pretty sure, too, that if Cole had been fit for Montenegro and Poland, he would have started, regardless of how well Leighton Baines has done."
England have not gone beyond the quarter-finals of a World Cup since 1990.