Gabriel Ameyi said the Tottenham Hotspur striker and the Stade Reims goalkeeper, Togo's highest-profile players, had been left off the list by coach Didier Six before last Wednesday's deadline for the submission of the 23-man squad for the tournament in South Africa, which starts on Saturday.
"I insisted to Didier Six on taking Adebayor and Agassa, especially after the meeting last week between Adebayor and President Faure Gnassingbe," Ameyi said in a statement on the Togolese Football Federation website.
Six had replaced Adebayor after meeting him just before Wednesday's deadline when the lanky striker reportedly told the coach he was no longer interested in playing.
Agassa was not included because he said he was injured, Six told French sports daily L'Equipe last week.
"I was surprised by this especially after the meeting Adebayor had with the president," said Ameyi. "I decided after a brief meeting to change it."
Agassa played for Reims in their Ligue 1 loss to Bastia on Sunday but told reporters before the match he would be joining up with the Togo team on Monday.
Both players had been involved in a proposed boycott of the side over unpaid bonuses.
Adebayor was persuaded back after meeting Togo's president last week, after which the striker described the running of Togolese football as "sick" and "in need of medicine".
A government emissary was sent to France to speak to Agassa.
Togo's first game at the Nations Cup is on January 22 against favourites Ivory Coast in Rustenburg.