He accepted an FA charge of improper conduct for his actions after his side’s defeat at Burnley last month.
Pochettino later said he was “in shock” at the “unfair” ban.
But the FA said Pochettino’s “repetitive and aggressive” actions merited a “sporting sanction”.
The FA’s written reasons for the ban included Dean’s match report, which said that the Argentine repeatedly told him “you know what you are, you know what you are”.
“I then said on numerous occasions to go away at least 10 times and he wouldn’t get out of my personal space and then aggressively pointed his finger just a few inches from my face again saying ‘you know what you are’,” Dean’s report added.
Dean said Pochettino confronted him again inside the tunnel before being escorted away by security staff.
The FA said it was a “persistent display of unacceptable and disrespectful behaviour”.
“While the words used are not the worst, the choice of phrase ‘you know what you are’ was used in an on-field outburst, following the conclusion of the game, that lasted for 40 seconds, during which Pochettino was, at times, very close to Mr Dean and face-to-face,” the statement said.
“Pochettino’s position is then aggravated by the fact of the second charge, which involved him waiting for Mr Dean in the tunnel area to resume his unacceptable comments.
“The commission finds as a fact that [Pochettino] did this quite deliberately.
“Such behaviour, at the elite level of English football, tarnishes the image of the game.
“Whatever decisions, and indeed whatever mistakes, may be made during a match, match officials are entitled to be treated professionally and with respect.
“They are not ‘fair game’ for a frustrated manager, or player, to vent their frustrations at.”
The FA said Pochettino’s “previous exemplary record, admission and apology” resulted in his ban being reduced from three games to two.
Pochettino served the first game of his touchline ban in Saturday’s defeat at Southampton and will also be in the stands for Spurs’ game against Liverpool on 31 March.