The striker was on target for the Baggies against Villa at Villa Park in the Premier League on Saturday afternoon.
The 22-year-old stuck out a foot to steer James Morrison's shot home from close range in the 39th minute of the encounter.
Berahino’s goal proved to be the difference between the two sides at Villa Park, as West Brom registered a 1-0 win in the West Midlands derby.
Fletcher has revealed that the youngster raved about his winner against Villa after the match.
"He did divert it for the goal,” the former Manchester United midfielder told FourFourTwo. “His words were it's a 'Zidane touch' and 'It was like Zidane', he felt that he meant it - you can tell he doesn't lack confidence.”
Berahino is one of the best players in the current West Brom squad, and he will be important for the Baggies as the season progresses.
The former England Under-21 international has not started the season brilliantly, but he has huge potential and will get better in the coming months.
Berahino has scored one goal and created two chances in four Premier League appearances so far this campaign.