Albion's top-scorer saw his second-half penalty saved by Kasper Schmeichel and Leicester then scored twice late on to claim a 2-0 win at the Amex.
It was Murray's second miss from the spot this season, after he blazed over in the 0-0 draw with Burnley in December, although he has netted four penalties this campaign.
Asked if his miss against Leicester will stop him taking penalties in the future, Murray said: "No, not at all. This is part and parcel of it. Obviously the Burnley one earlier in the season I missed the target, I haven't done my job.
"Kasper's done his job and he's done it well. That's the way I look at it. I got it on target and it's a good save.
"It is a mind battle. Obviously he watches me and I watch him. You are trying to second guess each other. That's always the case. A lot of it is luck. It just wasn't to be. He earned his money."
Murray felt Albion produced a much better performance than in their 2-0 defeat at Leicester in their second league game of the season and said: "Leicester's not been good for us as a team. I thought we were a different beast to the brand new Premier League team that went up to Leicester and went out with a whimper.
"I felt as though we controlled the game for large periods and on a different afternoon we could have won it. It was a very open, end-to-end game, which didn't really suit us."
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