British media have already begun listing potential replacements for the Dutchman, including former manager David Moyes, but Carragher felt none of the available candidates would be up to the mark.
"They're on a terrible run of form -- of course they are -- but you look at people who could replace him... it's nothing to write home about," Sky Sports pundit Carragher said.
"What I'd say about Ronald Koeman is that we're seven or eight games into the season. Ronald Koeman has been a Premier League manager for three years.
"There has been a lot of chopping and changing -- there are legitimate reasons (for fan frustrations), but he needs a lot more time."
Everton were expected to be top four contenders after spending over 140 million pounds ($185 million) in the transfer window but are 18th in the league with eight points in their nine league games after scoring just seven league goals.
($1 = 0.7570 pounds)
(Reporting by Aditi Prakash in Bengaluru; Editing by Ian Ransom)
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