The Brazilian was suspended for two games after clashing with members of Ipswich's security team following his team's 2-1 loss against their relegation rivals at Molineux on December 14.
Cunha elbowed a man and "knocked his glasses from his face, causing them to break", according to the panel's report, published Tuesday on the Football Association's website.
It said the "starting point" should be a three-match ban, to reflect the seriousness of the offence.
But it added: "The commission agreed that (Cunha's) acceptance of the charge, his prompt personal apology... the offer to pay for new glasses and his clean disciplinary record, were mitigating factors."
Those factors also helped to secure a reduction in the fine, from £120,000 ($150,000) to £80,000.
Cunha has been a standout player for Wolves this season, scoring 10 goals in 19 league games.
Defeat by Ipswich marked the end of the road for Wolves manager Gary O'Neil, who was dismissed and replaced by Portuguese boss Vitor Pereira.
Wolves are currently one place above the relegation zone, ahead of Ipswich on goal difference.
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