The former defender has hailed the Reds manager's handling of the 20-year-old.
Sterling, Liverpool's shining light so far this season (or at least one of them), had played a huge amount of football going into the busy Christmas period at Anfield.
Rodgers' solution was to allow the 20-year-old to take a winter break of sorts in Jamaica.
The result was a refreshed Sterling who scored a superb goal against Chelsea in the first leg of the Capital One Cup semi-final - one that could yet prove pivotal in the tie.
And Carragher feels Rodgers' handing of the young forward was smart management.
"Take Raheem Sterling. He was outstanding and Brendan Rodgers’s decision to give him a mid-season break in Jamaica was vindicated by his performance," Carragher said.
"Plenty of comment was made about Rodgers giving him a holiday but it was smart management."
Liverpool face Bolton Wanderers later today in the FA Cup and Carragher expects Rodgers to continue his shrewd use of Sterling by saving him for the second leg of the Capital One Cup semi-final.
The Reds head to Chelsea with a 1-1 draw after Sterling's equaliser but know they face an uphill task at Stamford Bridge, especially considering the Blues' away goal from the first encounter.