NEW YORK (CBSNewYork) — A day after Roy Halladay tweeted that Roger Clemens doesn’t deserve to go into baseball’s Hall of Fame, the former Yankees and Red Sox ace accused his former teammate of cheating himself.

On Tuesday, a day before this year’s class of Hall of Famers was announced, Halladay posted on Twitter: “When you use PEDs you admit your not good enough to compete fairly! Our nations past time should have higher standards! No Clemens no Bonds!”

Clemens indeed did not receive an invitation to Cooperstown. He, however, fired back at Halladay on Wednesday night, although he did not mention the retired pitcher by name.

“What is disheartening is getting a call or a text from family or friends about an ill informed player making an asinine statement. The last coming from a former Blue Jays pitcher,” Clemens said. “Just to enlighten him, he was accused of using amphetamines by the ‘strength coach.’ You should be very careful when putting tweets out while not having your facts on the matter at hand.”

Halladay responded Thursday, again on Twitter, writing, “I’ll let my reputation speak for itself.”

Clemens was named in the 2007 Mitchell Report, which documented illegal steroid use in Major League Baseball. The report alleged former trainer Brian McNamee repeatedly injected Clemens, a seven-time Cy Young Award winner, with an anabolic steroid.

The accusations, which Clemens has denied, are proving to be a roadblock to his possible induction into the Hall of Fame. He received support from just 45.2 percent of voters on this year’s ballot. Seventy-five percent is needed for election.

Mike Piazza and Ken Griffey Jr. were the only ones who received the necessary votes.

Clemens and Halladay, who won two Cy Youngs, briefly played together on the 1998 Blue Jays.