Brighi joined Atalanta on a season-long loan and the two teams are due to meet in the League next weekend.
Vanni Puzzolo told forza-roma.com: "Matteo would have stayed at Roma forever. He had, however, a great desire to play. When the opportunity to join Atalanta presented itself, he took it, having realised that with Luis Enrique [pictured] there would be no room for him.
"In Bergamo, Matteo is playing very well and has started the season on the right foot. I think that so far, Atalanta has played some great football, earning the results they have recorded.
"Nobody has ever lobbied for Brighi to get away from Roma because the guy is highly respected by both [Walter] Sabatini and [Franco] Baldini.
"Certainly, the tactical and technical vision of the Coach has weighed heavily in his decision. Matteo understood from the very beginning of the team's ritiro that he would not be part of the project."