Rodgers's side followed up a 4-0 win against Everton last week with a 1-1 draw with West Bromwich Albion on Sunday, and the Northern Irishman thinks that his charges put in a finer quality of performance for the higher-profile matches.
Rodgers told reporters: "I feel that the bigger the games are, sometimes, the better we play. Against Tottenham Hotspur, Everton and Manchester United we showed that.
"We're really looking to show our confidence and belief and put in a performance that is going to get a win for us.
"We've been brilliant at home. The performance level from the players and the support that the fans have produced over the majority of the games has been outstanding. So it's another big game for us."
Victory against the Gunners would extend the Reds' grip on fourth place to five points.