The 23-year-old collapsed during the FA Cup quarter-final between Tottenham Hotspur and Bolton Wanderers, but the Trotters midfielder is showing encouraging signs of recovery at the London Chest Hospital.
The British No1, who is preparing for the Miami Masters, believes that not enough is being done in tennis, and sport as a whole, to ensure such incidents are avoided.
“I was actually watching the game when it happened and I was head in hands,” Murray told MSN Sport.
“You just can’t believe it. It’s an amazing fight from him and hopefully he’s going to make a safe recovery.
“It should be something that’s just done,” he added. “I think it’s time in almost all sports everybody should have screenings before they can compete.
“This has happened too many times. Here in the States it’s happened in high school and college basketball games and, of course, it’s happened a few times in football.
“With all the pressure and stress of modern sport you have no idea how much you are pushing yourself on the pitch or court, I think it’s something that’s just got to be done.”
The 24-year-old world No4 also revealed that he has his heart checked independently on a regular basis – but the Scot believes it is something which should be made compulsory.
“I do my tests independently,” he said. “I’ve been doing my tests for three years now so I have heart scans, heart monitors and other tests. I started when these things seemed to be happening more often.
“But it’s not something that’s done within tennis. But I just think it should be. Everyone should have a medical or a check-up before you’re allowed to compete because it’s such a horrible thing for people to witness.
“The reality is if something doesn’t happen about it, it’s likely to happen again at some stage, and it’s just so, so horrible. You don’t wish something like that to happen to anybody.
“It’s clear to me that all the teams should be checked. I’m not sure if they do, but I know in tennis we don’t.”
MORE: The latest football news
MORE: The latest tennis news