The left-hander was struck on the neck by a short ball while playing for South Australia against New South Wales in the Sheffield Shield on Tuesday.
After being taken to hospital, Hughes underwent surgery but failed to wake from an induced coma, and his death at the age of 25 was confirmed on Thursday.
Tributes have poured in from the cricketing fraternity, with Yorkshire head coach Gillespie, who took 259 wickets in 71 Test appearances for his country, left stunned by the news.
"We're all devastated," he told Perform. "At our club here and in the UK, we're devastated at the passing of Phillip Hughes.
"I can't imagine how everyone is feeling back in Australia. It's a tough time for everyone and our thoughts are with everyone back in Australia.
"He was a fantastic young player, he performed in all parts of the world. To see his life cut short like this is upsetting and as I said, our thoughts are totally with his family and friends at this time."
Australia are due to take on India in Brisbane in the first of four Test matches next week, but Gillespie is unsure whether the series will go ahead.
"I'm not the person to answer that, I can't imagine going out and playing a game of cricket in these circumstances," he said.
"Who knows whether the Test match will be going ahead or not, at this point of time the focus is on the family and friends of Phil Hughes and we can't really think too much further than that to be honest.
"He was a lovely lad. I spent a bit of time with him, he was a great kid and for this to happen...I can't quite comprehend it to be honest.
"He was a very good young player and I just can't believe he's not here now."
Hughes' death has raised questions over safety in the sport, but Gillespie says dealing with such issues should be left for another time.
"With all due respect, now is not the time to think about that," he said. "There's a grieving family back home, it's a really sad time and there's a time and a place to talk about that.
"It's going to be a very difficult time for everyone. At the moment the focus is on being very supportive of his family and friends."