The Reds are focused on regaining a top-four Premier League place this season but also want to do well in the domestic cups ahead of a difficult clash with the Potters at the Britannia Stadium.
Gerrard wants to be back in the Champions League but he has also stressed the importance of winning silverware.
He told the LFC Magazine: “Getting back in the top four is a priority, but I wouldn’t say it’s our only priority.
“Bringing those European nights back to Anfield is what we all want. Some of the best nights of my career have been in the Champions League and I want to experience a few more before I eventually hang up my boots.
“At the same time it’s about trophies for me and I see the FA Cup and Carling Cup as also being very important. Because we are only involved in three competitions we have to focus on all of them.”
Liverpool have a miserable recent record at Stoke and were beaten 1-0 by Tony Pulis’s side in September but Gerrard hopes they can finally win in the Potteries as they aim to keep on track for a Wembley appearance in February.
“There is no European football so you can afford to focus more on the Carling Cup,” he added.
“We haven’t done well in any of the cups domestically since 2006. It’s time we gave the fans a bit of excitement again. They deserve it and there would be nothing better than going to Wembley. That would be fantastic for everyone.”
Derek McInnes wants his Aberdeen players to dare to dream as they look to grab their first win in 10 attempts against Celtic.
Brendan Rodgers is looking for Celtic to move on from their Europa League exit when they return to Ladbrokes Premiership action at Aberdeen on Sunday.