Saints were the only English side to reach the quarter-finals of the competition last year - where they lost 33-19 to Munster - but Mallinder is convinced it will be a different story this time around.
"There's general disappointment at how the English clubs did last season," he said.
"But you look at the teams in the Cup this season, and most of them are doing well in the Premiership.
"We have to step up now - we want to repeat our successful Heineken Cup campaign from last season and go a stage further.
"Castres is a tricky game. We've seen them at home and away, and they're a good outfit. Last year, we had Munster at home in the first round, and the crowd got behind the team.
"We hope to recreate that atmosphere and result."
Elsewhere Leicester travel to Italy to take on Benetton Treviso, Brendan Venter takes his Saracens side to France to face Clermont Auvergne while Aviva Premiership leaders London Irish host Munster at the Madejski Stadium.