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."
Alonso, who did not play in the final due to suspension, ran down to the pitch from the stands in Lisbon when Gareth Bale put Real Madrid ahead in extra-time.
And the Spaniard claimed he felt more comfortable in the team set-up in recent years than he had in the past.
"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."
