Carrick is under pressure after Manchester United's 2-0 Champions League defeat to Atletico Madrid in midweek. United have also struggled in the Premier League, recording just one league victory in their opening six matches.
Leeds, meanwhile, have made a positive start to the season, collecting nine points to sit seventh in the table. Farke has also been linked with a new contract, highlighting the contrasting situations facing the two managers.
Despite the scrutiny surrounding Carrick, Farke believes the young English coach deserves greater recognition for his work at Manchester United and previously at Middlesbrough.
"When I think about Michael, we don't have too many young British coaches and managers in the Premier League," Farke told reporters.
"Right now we have someone, a really young, promising manager who has done an excellent job at Middlesbrough."
Farke also praised Carrick for stepping into a difficult situation at Manchester United last season and helping to stabilise the club.
He was particularly critical of the speed with which the criticism had started, given that only six league matches had been played.
"After six game days, when they didn't have a horrendous start but, of course, by their perception they want to fight for the title, the criticism starts already. I don't like it," Farke said.
"If we have young, promising managers, let's also look a bit after them, especially ones that have a British passport."
The Leeds manager also reminded critics of Carrick's long association with Manchester United, both as a player and as a coach.
"Keep in mind what he has done for the club for many years as a player, what he has done last season in a very difficult situation where many people would also be a bit hesitant to step in and to help.
"He has done a top-class job."
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