Jurgen Klopp handed his January signing a first start for the Merseyside outfit in their FA Cup fourth-round clash at Anfield.
Caulker partnered Dejan Lovren at centre-half as the 18-time English champions managed to keep a rare clean sheet under Klopp.
The one-time England international is vying for a first-team spot with Lovren, Kolo Toure and Mamadou Sakho, with Martin Skrtel still to return from a hamstring injury.
However, Caulker impressed former Manchester City forward Marsh after he took to Twitter to heap praise on the Liverpool signing.
Any one notice how excellent Caulker was today ?
— Rodney Marsh (@RodneyMarsh10) January 30, 2016
Caulker moved to Liverpool on loan until the end of the season from Championship side Queens Park Rangers.
He earned his only England cap in 2012 but the centre-half has failed to build on his early promise at Tottenham Hotspur.
Caulker has previously played for Cardiff City and Southampton and he moved to QPR in 2014 but was unable to help the west London side avoid relegation.
The Liverpool man has also had loan spells at Yeovil Town, Bristol City and Swansea City during his spell at Spurs.
MORE: The latest football news