The 20-year-old accepted a violent conduct charge from the FA.
The 20-year-old midfielder receieved three-match ban after accepting a charge relating to an incident in which he appeared to punch West Brom's Claudio Yacob in the stomach during Monday's 1-1 draw at White Hart Lane.
The England international will miss Spurs' end-of-season run-in as a result of his actions, which makes their Premier League title bid even more unlikely given the fact they already sit seven points behind Leicester with only nine points left on offer.
And Roberts says that the likes of Vertonghen and Dembele, relatively experienced outfield figures in a young Tottenham side, should have put an arm around Alli, who has garnered a reputation as something of a hot head despite his "wonderful talent".
"We needed one of the experienced players like Jan Vertonghen or Moussa Dembele to get hold of him and just say 'look calm down'," Roberts told Sky Sports. "West Brom did their homework. They got Yacob on him and he was winding him up from the first kick of the game.
"He tackled him, he pulled him, he pushed him over, but being 20 years old you just get a little eaten up about it. I don't think there was anything in it anyway.
"He has just swung an arm and caught him. He's got to learn from that because there will be other teams in Europe, in the Champions League, when we get there, and in the league next year, who will all be trying to wind him up. He's got to learn, but he's a wonderful talent."
Alli, who was crowned PFA Young Player of the Year on Sunday, will miss Monday's trip to Chelsea, the visit of Southampton and Newcastle United away on the final day.