"To me, personally, I think you should be out of the game if you get caught," Trout said Monday during an interview with New York radio station WFAN. "It takes away from the guys that are working hard every day and doing it all-natural."
Rodriguez currently is appealing a 211-game suspension, which runs through the 2014 season, for violating Major League Baseball's drug policy. The three-time MVP has appeared in five games this season with the New York Yankees and homered in Sunday's victory over the Detroit Tigers.
Trout, the American League Rookie of the Year last season, told WFAN that he is frustrated by players who use performance-enhancing drugs.
"Some people just are just trying to find that extra edge," Trout told the radio station. "It's tough as a guy that goes out there and plays hard every day and puts [in] 110 percent effort ... to wake up, see there's a list of guys that are on the list. It's good that MLB caught them and they're moving in the right direction with suspensions and stuff."
Trout and the Angels will start a four-game series against the Yankees on Monday in New York. He declined to reiterate his comments later Monday in the Angels' clubhouse, repeatedly deflecting questions to team player representative C.J. Wilson.
"You're going to have to talk to C.J., our rep in the clubhouse," Trout told reporters. "I don't want to talk about it anymore."
The 22-year-old Trout, who is batting .330 this season with 20 home runs, 73 RBIs and 26 stolen bases, did tell reporters that he thinks it is important for young players to pave the way for a cleaner game.
"We get tested every day, every week," Trout said. "As young guys like me, [Bryce] Harper, [Manny] Machado, [Yasiel] Puig, guys that go out there play hard and that's good for the game."
Angels slugger Josh Hamilton agreed with Trout, claiming that the overwhelming majority of players want strict penalties for PED users.
"That's [what] I would say 95 percent of the guys in the league want -- even playing field, guys coming out here working hard and all-natural and going out there and playing the game," Hamilton told reporters. "I think [Trout] is right on."
ESPNNewYork.com's Matt Ehalt contributed to this report. Mike Mazzeo is a regular contributor to ESPNNewYork.com.