The Hammers make the trip to Turf Moor tonight to face the Championship leaders in the fourth round.
Despite Burnley's good form this season, Tomkins is hopeful that West Ham can do enough to advance.
"Burnley's going to be difficult as they're on fire at the minute in the league, but we go there full of confidence, because we've put in some good performances in the League Cup and hopefully that continues," he told the club's official website.
"Every game's a massive game, hopefully we can go out there, start well and put them under pressure.
"We've played them a couple of seasons ago in the Championship and it's always a difficult place to go to, but that's something we're looking forward to."
West Ham were beaten 4-1 by Wigan Athletic in the third round last season.