Benteke and Mandanda both started the cup clash at Selhurst Park, with Scott Dann scoring the opener via a deflection to send Palace into half-time a goal ahead.
The club's £27million record signing was substituted at the interval for Connor Wickham, who scored soon after the break to secure progress to the third round of the competition after the club's poor Premier League start.
Pardew told the club's official website: "We're through, [have] no injuries and a couple of good debuts. Benteke showed why we paid a record fee and Mandanda showed why he was Marseille captain.
"Christian's arrived and taken a bit of weight off Connor. He looked fresher, sharper for it.
"We erred on the side of caution tonight with Christian. He's still getting up to speed.
"I want Christian to get to the level where he was prior to Liverpool. He didn't play enough there, but he'll get a flow of games here."