"I have informed Saido that he will not be transferred during this summer window," Peace said.
The chairman's comments did not go down well with Pochettino, whose club have reportedly had two bids of 18 million pounds ($28 million) and 22 million pounds for the forward rejected already.
"It's like when you are in love with some lady," Argentine Pochettino was quoted as saying by the BBC.
"There are a lot of women around the world, but you want only one. Sometimes it is impossible. It's about love. And in football it is the same."
West Brom have already rejected a written transfer request from Berahino, who was dropped for the 3-2 home defeat against Chelsea at the weekend as well as for the League Cup penalty shootout win against League One side Port Vale on Tuesday.
The Burundi-born forward scored 20 goals last season and Peace criticised both the timing of Spurs' move and their valuation of the player.
"As I have made clear from the moment Tottenham lodged their first bid for Saido on 18 August, selling our top goalscorer was never on our agenda this summer," Peace said.
"Not only have the offers been too low... but they have been based on stage-payments and add-ons over a long period which do nothing to reflect Saido's ability and potential.
"I have the greatest respect for Spurs chairman Daniel Levy but he must surely appreciate we would have needed to replace Saido... and no consideration of that position has been reflected by Tottenham's strategy," Peace added.
"It has contributed to our completing our last two games without a key player.
"I have spoken to Saido... he has been unsettled and distracted by all this and I understand that. But I have strongly advised him to put this behind him."
(Reporting by Simon Jennings in Bengaluru; editing by Sudipto Ganguly)
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