Following an up-and-down season last year, which ended when they lost to Glasgow Warriors in the PRO12 semi-finals, Munster currently sit fourth in the league table after six games.
Murray has been a key cog as the Red Army adjust to life under new head coach Anthony Foley, who replaced previous incumbent Rob Penney over the summer.
And the Ireland international is adamant that Munster are going from strength to strength and putting past demons behind them.
"We're starting off with a new coaching staff and a new game-plan," said Murray. "The players have huge belief that we can execute that quite well.
"And we're starting to - against Leinster was the time when we really dominated the breakdown and really looked good. Other games we've played quite well.
"We could get up for the big games in the last two years and then in other games we were too inconsistent in putting away what we would regard as weaker sides.
"We're looking for that consistency this year. The belief is there in our players that we can execute the game-plan and be contenders. We need to find it within ourselves to perform consistently."
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