The 36-year-old says he received "foul" abusive messages after Somerset lost to Glamorgan by one run on Sunday.
And he believes the shorter form of cricket is to blame for "bringing a lot of idiots to the game".
However, former England captain Michael Vaughan says players must learn to take social media abuse "on the chin".
Trego, who made his first-class cricket debut 17 years ago, said one expletive-strewn message sent by a boy on Instagram this week was "one of the most abusive messages I think I've ever read in my life".
The post, which Trego has not reported to police, branded the cricket veteran as "useless" and also urged him to quit the sport.
Speaking to BBC Somerset's cricket reporter Charlie Taylor, Trego said: "To send professional athletes, who are giving their best, abusive messages is just an absolute disgrace, and unfortunately I think it is a little bit en vogue at the moment for young people to feel like that's OK."
He added: "When it gets to what I would call football hooligan abuse level, I just think, is that really what we want for the future of our cricket?
"I know [the T20 game] brings in a lot of money, a lot of revenue, a lot of excitement. But it's also bringing in a lot of idiots to the game who might be spoiling other elements of our game for the next generation."
But former England batsman Vaughan claims social media is making this the hardest era for players because there is no respite from criticism.
The 42-year-old said: "For a fan to be able to direct message their opinion to you, whatever that opinion may be whether it's good or bad, I would say to players you've got to do one of two things.
"You've either got to take it on the chin, you've got to accept that's the modern world. Or don't look at your phones."
Somerset all-rounder Peter Trego says the abuse directed at players in Twenty20 cricket has reached "football hooligan levels".