"Winning our first four games set us on our way," the Arsenal goalkeeper said in an interview a day after his team became the second country to qualify for the finals, following England.
Sunday's 2-1 win over hosts Latvia in Riga ensured them a top two finish in Group A but Cech said confidence in the youthful team's ability had come early when they beat the Netherlands in their opening qualifier in September last year.
"Beating the bronze medallist from the World Cup in our first game gave us that belief that we could compete," Cech said.
"We had a new team and we hadn’t had much success in our preparatory games. Holland was our first big test and we won and suddenly we realised we could compete with the best teams and had a chance in our group.
"Then we put together four wins in a row and we had a foundation."
Equally important was the victory in Prague last week over bottom-placed Kazakhstan, he said.
"When we dropped two home points at home against Latvia (in March), everybody said 'ah, the machine got stuck'. Then we lost in Iceland (in June) and everybody was expecting us to panic and experience a difficult time.
"Against Kazakhstan we were 1-0 down and we had to really dig deep to get the win, showing this team has the will and character to overcome difficult moments." It left the Czechs needing victory in Latvia to ensure a place in next year’s finals, which they achieved despite a nervous final stage as Cech thwarted several home attacks.
"With my experience and with players who had never played such an important match before, you could see in the second half it was important to keep calm to give confidence to everybody around and to make sure we go through.
"The last 20 minutes were very tough because mentally we were a little anxious."
For Cech, it is a return to the European Championship finals after previous appearances at the 2004, 2008 and 2012 tournaments. He also competed at the 2006 World Cup in Germany and with 115 caps is the father-figure in a young team.
"I'm not sure yet what the potential of this team is," the 33-year-goalkeeper added. "We are happy to qualify and we have three quarters of a year now to prepare. Let’s see what will happen."
(Editing by Amlan Chakraborty)
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