Gruden, who at the time was a broadcaster for ESPN, told the WSJ he didn't "specifically recall writing the email" -- but he added he was still "really sorry" for it.
"I was upset," 58-year-old Gruden said. "I used a horrible way of explaining it."
"I don't think he's dumb. I don't think he's a liar,” Gruden added. "I don't have a racial bone in my body, and I've proven that for 58 years."
Gruden went on to say he had, in the past, called liars "rubber lips" and went "too far" in his message about Smith to Allen.
What's interesting, NFL sources tell TMZ Sports the email was found by league investigators while they were conducting a probe into allegations of workplace misconduct in the Washington Football Team organization.
They added the league is currently investigating the matter.
Smith, meanwhile, told the WSJ he was disappointed to learn of the comments Gruden wrote behind his back ... explaining, "Racism like this comes from the fact that I'm at the same table as they are and they don't think someone who looks like me belongs."
"I'm sorry my family has to see something like this but I would rather they know. I will not let it define me."
The Raiders -- who hired Gruden away from ESPN to be their head coach in 2018 -- have yet to comment.