The Football Association has launched an investigation into Cavani’s social media post following United’s 3-2 victory over Southampton on Sunday.
The Uruguay international responded to a post from a friend on Instagram saying, ‘Gracias negrito’, which translates as, ‘Thanks, little black’.
Cavani deleted the post after he was made aware that the word ‘negrito’ is interpreted differently in the UK as opposed to his homeland, where it is used as a term of endearment between friends.
Cavani is facing a three-game ban if the FA decide to act.
But when asked if he thinks a three-game suspension is enough for Cavani, Deeney told talkSPORT: ‘No, I don’t think it is.
‘It’s a considered post. He’s written it out, thought about it, and he’s got people around him who would say, ‘I don’t think you should really do that’.
‘He’s probably acted in a moment of happiness, obviously after scoring, that’s why I don’t take it as he meant offence by it, he just hasn’t understood the ramifications of his words.
‘I do think at times three games isn’t enough, because it’s got to be three games with a form of education in my opinion.
‘There needs to be an understanding that these words hurt people and the reasons why they hurt people.
‘I’d be very interested to see what Patrice Evra has got to say on it.
‘It’s never right, no matter which way you look at it.
‘I just think when you write a message out, it’s considered, nine times out of ten, that you’ll proofread it before putting it out there because you don’t want to make yourself look an idiot.
‘I understand we get three-game bans now, but I just want to know whether the FA are educating players when they come to this country.
‘I don’t think he’s meant it to insult anyone, but he needs to be educated on what is acceptable and what isn’t.’