Dithejane cracked the preliminary 54-man squad for the Africa Cup of Nations, only to be among the harsh final cuts as Broos reduced the group to 25 ahead of this month’s tournament in Morocco.
Beganovic concedes the youngster was always facing an uphill battle but believes the 21-year-old still has time – and talent – to compel a rethink from the national coach.
"I think Puso has improved a lot this season, and he's also close to catching that call to be in the squad, but sometimes we also need to understand that players who play and qualify for the World Cup and AFCON deserve more chance to be there," defended Beganovic.
"Because they [were the ones who] fought for that and then they obviously need an opportunity to be there, but Puso is still young and I think in the next period he will be one of the real Bafana Bafana players."
The coach added that part of his mandate at Galaxy is to produce young players that can ultimately represent their national teams.
"It's unbelievable because since I've come into the club three years ago, we tried to produce players to put them on the market, and also for Bafana Bafana [because] it's very important for the club," he noted.
"Still he is young and we have a young squad, and for me we can talk about everything, but other coaches say TS Galaxy belong with the three clubs based on their performance on the field, how we play tactically and look technically on the field.
"I can be so proud, but that means we must push well and improve our players all the time, and then we will produce players for Bafana Bafana."