Speaking to TMZ Sports, Taylor noted Winston needs to be smarter about the choices he makes.
"Especially with the problems he's had you'd think he'd make better judgments than that."
ESPN.com's Adam Schefter reported Winston will be suspended for the first three games of the 2018 season for violating the NFL's personal conduct policy, stemming from a 2016 incident in which he was accused of sexually assaulting a female Uber driver.
Taylor also addressed Winston's accuser, saying he hopes "it's not a situation where someone wants to be in this #MeToo genre."
A woman, identified as Kate, told Buzzfeed's Talal Ansari last November that Winston "reached over and he just grabbed my crotch" after she picked him up around 2 a.m. outside of a nightclub in Arizona.
Philadelphia Eagles cornerback Ronald Darby, who played with Winston at Florida State, said in a statement after the allegations came out that there were "three of us in the car, not just one as has been reported," and he was "confident that nothing inappropriate in nature happened" between Winston and the Uber driver.
Per NFL Network's Mike Garafolo, the league's investigation found Darby's statement flawed because he wasn't in the car the entire time.
If Winston serves a three-game suspension, he will be eligible to return for Tampa Bay's Week 4 matchup against the Chicago Bears on Sept. 30.