The club won their first Scottish Premiership title in a decade last month but have since been knocked out of both the Europa League and Scottish Cup, but Gerrard suggested it would be a "cop-out" for the team to blame it on their title glory.
He said: "I think it's the easy way out, a cop-out, for us to use excuses from three or four weeks ago.
"We felt fantastic back then and there was a lot of relief and emotions. Rightly so, we deserved that.
"But I made it clear the Scottish Cup was a priority and we needed to keep hungry. A lot of this game was alright. We had the best chances but you need to take them, or you get stung at the end of games."
Rangers were knocked out on penalties by St Johnstone and Gerrard suggests it shows that his team still have work to do.
He said: "Credit to St Johnstone, they got one moment and then it was on to penalties. We need to take responsibility for this and we need to be better in cup competitions moving forward.
"We have never said we are the finished article. We always have one eye on how we can improve.
"That goes for me as well. I am really disappointed with how this has ended and I will reflect on how I can get this group better.
"We need to be better prepared for cup competitions moving forward and we will be back stronger next season.
"But there will be no shying away from us taking that responsibility and I see loads of areas where we can improve. We will keep striving to do that."