Alonso's side won the UEFA Champions League final over Atletico Madrid on Saturday night, courtesy of a 4-1 victory - with those egos getting a boost as they delivered Real's 10th European Cup.
The former Liverpool man said Real's dressing room was stacked with self-confident players but claimed coach Carlo Ancelotti kept them all in check.
"In the dressing room there is so much spectacle, there are clans, but usually they have a good relationship with each other," Alonso told Canal+.
"The egos are managed well."
"If I have to yell at Cristiano (Ronaldo), I yell. I wouldn't have yelled at (former Real midfielder) Zinedine Zidane five years earlier," he said.
Alonso said Real's squad were making history for the club, and the 32-year-old added he was not anticipating having to leave the team for good.
"Being in this group means a lot. The generation we have had is a blessing, it's history. There is no cause that has united us like this," he said.
"It's hard to imagine being an ex-player. It's not easy to find a new passion."
