The 36-year-old wrote in his column in the Daily Mail that both clubs should not let their desire for European success "cloud the big picture" - as a historic season is still possible for both sides domestically.
Indeed, both Manuel Pellegrini and Arsene Wenger's sides can still lift FA Cup and Premier League trophies this season, with their Champions League seasons on the brink after 2-0 first-leg defeats to Barcelona and Bayern Munich respectively.
Carragher thus feels Man City and the Gunners should rest key players for their second-leg clashes, both of which will be abroad, and prioritise domestic action.
"The Champions League is an obsession for all managers but an obsession cannot cloud the big picture for City and Arsenal," he wrote.
"With that in mind, Pellegrini should consider not taking his key players — men such as Vincent Kompany, Sergio Aguero, Yaya Toure and Joe Hart — to the Nou Camp on March 12. Similarly, Wenger would be better served leaving his top men at home when he heads to Munich 24 hours earlier.
"As hard as that might be to hear, consider this: no team in the history of the Champions League have ever overturned a 2-0 home defeat away in the second leg. City had enough trouble laying a glove on Barcelona at home, so what realistic chance do they have of scoring three away?
"To win the title, you need your best players available for the biggest games. Manchester City and Arsenal can maximise their chances of that by giving their main men an evening off in the middle of March. The reward could be a Treble or a Double."
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