Hibs play host to Derek McInnes's men this weekend and are hoping to get back to winning ways following the disappointment of defeat to Inverness last Saturday.
The Perth outfit beat Aberdeen last weekend to bring to an end a miserable run of five defeats on the bounce in cup and league competition.
Despite having taken just 14 points from 14 games this season, the McDiarmid Park side have played some decent football without being able to produce the end product and two of the mainstays of their starting line-up have been Morris and former Chelsea team-mate Michael Duberry.
The duo have a wealth of experience behind them and come with big reputations, but Murray is certain that Hibs have the strength and quality of their own to make sure they head back to Perth empty-handed.
Murray said: "Jody Morris is a neat and tidy player and gets himself stuck in even although he is not the biggest of guys. He has obviously got a lot of talent and everyone will remember him from his Chelsea days.
"He can spray the passes about no problem at all but, in terms of St Johnstone and their midfield, I feel that we have got the players to deal with him.
"I think we have got the team that can win."
And Murray added: "I know that they got a good win up at Pittodrie last weekend but we are at home again.
"We have got a decent run of fixtures heading towards Christmas so, hopefully, we can get a good result."