When Cech joined Chelsea ahead of the 2004/05 season, he ousted Cudicini, the club's first-choice goalkeeper at the time.
"It was a huge disappointment for me at the time," the former Italy goalkeeper admitted.
From his own experience, however, he knew that rivalry between goalkeepers could be destructive and did not want to create a similar environment at the Blues.
"When I was a youngster at AC Milan, there was huge rivalry between Sebastian Rossi and Francesco Antonioli, and it got quite ugly at times," explained Cudicini.
"When a similar situation later happened to me, when I was not playing and was unhappy, I told myself that I did not want to behave like that. The only way to prove my worth was to train as well as possible," he said, describing his approach to the competition.
The two goalkeeping legends agreed that their rivalry helped both their performances and Chelsea's overall success.
"Over the years, we built a very good goalkeeping group. Whoever was in it, we worked together brilliantly," Cudicini recalled.
The full television version of this episode of the Big Pete documentary series will be available on CANAL+ Sport and the CANAL+ streaming service in the Czech Republic, Slovakia, France, Poland, Myanmar, Belgium, the Netherlands, Austria, Romania and Hungary, and on SuperSport in South Africa and Switzerland.