The Scot booked his place in the last eight with a three-set win over the experienced Youzhny, but Murray insists that he is not taking anything "for granted".
"It was a tough match, the first couple of sets especially, but once I got ahead in the third I concentrated hard on not letting him back in like I did in the second set," he told BBC Sport.
"I don't take anything for granted. I know how hard these tournaments are to win. There are no guarantees here and I don't come into them thinking I am going to win.
"I think a few rounds ago I was more nervous but today I felt calmer before the match. I just concentrate on each game. Serena [Williams] lost today, Roger [Federer] has lost and Rafa (Rafael Nadal) has lost, so you cannot take anything for granted."
Murray was beaten in the final of Wimbledon last year.