The commentator made the remark last night during the BBC's coverage of England's quarter-final match against Italy.
After Guy Mowbray invited viewers to tweet about the game, Lawrenson replied: "If you're sad enough, you can."
Mowbray himself is a user of the site with over 20,000 followers, while BBC pundit Gary Lineker has posted over 4,000 tweets to his 811,000 followers.
"I don't mind that Mark Lawrenson labelled Twitter users sad," said Bill.I.Am. "I just hate his inane bad-joke based commentary that has little insight or wit."
"'Un-sad' Mark Lawrenson isn't on Twitter as we now know so he won't have seen the thousands of people who are cheerfully calling him a .....," quipped Giles Dilnot.