Mel's men looked home and dry after their blistering opening 10-minute spell with goals from Morgan Amalfitano and Graham Dorrans.
But Jordon Mutch gave Cardiff a glimmer of hope before Steven Caulker's header levelled things up.
Then, just moments after Thievy Bifouma looked certain to have grabbed a first home win for Mel, substitute Mats Moller Daehli grabbed a point for Cardiff after Berahino gave the ball away on the break for Albion.
"I think there was one team who deserved to win the match and that was West Brom," the Spaniard told Sky Sports.
"Saido wanted to go on and score the fourth goal which is a good thing, but he is a player who in the future will go on to learn, and we believe he will become a very good player.
"The changing room is quite bad but they will see tomorrow that we played a good game and the result should have been a better one for us.
"Simply by showing the players the video of the first half, and showing them how well they played, they will be able to see how capable they are of playing well."