Monk played under Rodgers at Swansea, and the two came face-to-face at Anfield on Sunday, with Rodgers' Liverpool prevailing 4-3 in an enthralling encounter.
Since guiding the Welsh club to a 3-0 victory over fierce rivals Cardiff City in his first match in charge, Monk has overseen a Premier League draw at Stoke City, defeat in the FA Cup at Everton and Thursday's goalless draw in the UEFA Europa League with Napoli.
The Liverpool defeat leaves the Welsh outfit 12th in the table, four points clear of the bottom three, and Rodgers was insistent in his belief that his former player would show the strong work ethic needed to pull his team away from danger.
"He's been brilliant, he's been absolutely first class," he said.
"He's a good man and he'll be up from early morning until late at night making Swansea successful.
"He's been thrown in at the deep end with no experience and I think how he's dealt with it has been fantastic, really calm.
"You see the players work for him and of course over time, the real questions gets asked, 'is he a manager?' because you deal with other issues and the honeymoon period is over.
"But so far the team have been a credit to him. Garry's a guy that can really carry the club forward. I hope that he gets a continued chance to build his career as a manager."
