Augousti says on Celtic's official website that Phunya Sele Sele are serious about contesting for honours this season, and wanted to build the team round Mathoho.
"We seriously need to contest for a top four position and win a knockout competition in the new season," Augousti tells the club's website.
"We never really wanted to sell Mathoho until we received a written transfer request from his agent Tim Sukazi, which stated that the player would like to leave the club to join Kaizer Chiefs.
"We unearthed Mathoho and it was sad for us to say goodbye to him. We wanted to build the team around him. Unfortunately the Gauteng clubs filled up his head with 'cellphone numbers' in terms of money and he wanted nothing but to leave the club.
"When a player gives you a written transfer request saying that I want to go to Chiefs that really tells you that the player doesn't want to be in the team anymore."
Augousti insists, however that it is "not Celtic's policy" to stand in a players way, and wishes him all the best at Chiefs.
"We can't risk keeping a player whose mind and heart is no longer with the club, and he is just going through emotions. We would rather work with committed, hungry players who want to achieve success and take the club somewhere.
"We will find a replacement for Mathoho soon. Having said all that, we would like to wish Mathoho everything of the best with his career endeavours."
Turning to the new season, Augousti says Celtic have a tough first match against Orlando Pirates, a team full of "quality" in every department.
Celtic take on Pirates, provisionally, in the MTN8 at the beginning of August.
"However, it will be 11 against 11 on the day. I think with the team that we have assembled we are going to give Pirates a good run for their money," Augousti says.
"It will be important for us to get off our new campaign to a winning start. We want to improve from last season. We want the team to give the supporters something to cheer about by winning a trophy. We also want to bring back people to the stadium by playing entertaining football."