He said: "I can't condone death threats. It's ridiculous and something I can't stand by."
Adams spoke of the abuse that came his way in his playing days.
He was often the subject of taunts from supporters when he captained Arsenal.
The Blues manager relived being pelted with carrots after being labelled a donkey in the national media.
Adams also told the Portsmouth News: "I've never had to deal with what Jermain has.
"I've had a few carrots thrown at me in my time, and there were a few people who didn't like the way I played when I went around the country.
"The better I was playing the more the opponents were booing. But death threats are separate and I can't condone it."