The panel's 63-page findings were published a week after the verdict, and Terry has 14 days to decide whether to appeal against his four-match ban and 220,000-pound ($356,000) fine in English football's highest-profile racism case.
Although Terry was cleared in a criminal court in July, an FA panel with a lower burden of proof found the former England captain guilty of directing abuse at Queens Park Rangers defender Anton Ferdinand during a Premier League match last October.
Terry, who quit the national team before the verdict, maintained that he only used the slur to counter an accusation of racism he claimed Ferdinand was levelling at him.
But the FA commission concluded that aspects of Terry's defence were "improbable, implausible and contrived, and which serve to underline and reinforce our decision."
"The commission is quite satisfied, on the balance of probabilities, that there is no credible basis for Mr. Terry's defence that his use of the words '(expletive) black (expletive)' were directed at Ferdinand by way of forceful rejection and/or inquiry," the FA report said. "Instead, we are quite satisfied, and find on the balance of probabilities, that the offending words were said by way of insult."
The panel said "inconsistencies" in evidence from Terry's Chelsea teammate Ashley Cole showed there is "plainly more than enough cumulative evidence" for the verdict.
In an initial interview with the FA last October, Cole did not say he heard Ferdinand use the word "black." But Chelsea later asked the FA to insert the word "black" into Cole's witness statement, suggesting he might have heard Ferdinand use the term.
Cole's court testimony prompted Anton Ferdinand's brother Rio to post a racist gibe about him on Twitter. As a result, the Manchester United defender was fined 45,000 pounds ($73,000) by the FA in August.
In the Terry judgment issued Friday, the panel raised concerns about the long-term impact of the player's high-profile outburst.
"His conduct undermines the FA's efforts to promote inclusivity, equality and diversity and in combating racism in football," the FA said, while stressing that Terry is not racist.
Since the confrontation, Ferdinand has been taunted by Chelsea fans when QPR has played its west London rival.
"The victim impact statement of Mr. Ferdinand makes it plain that he has been badly affected by the incident," the FA panel said. "He has been the subject of hateful abuse and adverse comments, but has acted with restraint and dignity."
Rob Harris can be reached at http://twitter.com/RobHarris