Elimination from the FA Cup leaves Liverpool fighting on one front for the remainder of the season, the Barclays Premier League, and reporters questioned if that scenario could aid the Reds' push for success in the league.
Rodgers responded: "It doesn't feel like that now because we want to play and we want to be in as many competitions as we can. But I suppose it narrows our focus now to one competition.
"We'll just continue with the confidence and the belief that we have been playing with. You saw it today and if we play with that aggression, we're going to have a really exciting 12 games to finish the season.
"But I wouldn't like to say that we want to be out, because it was a competition that we wanted to get to the final of. Unfortunately, we've lost, so congratulations to Arsenal, who go through. We've got to go home and lick our wounds."