The assistant manager has paid homage to Giovanni Trapattoni and states his belief that the Irish players have improved markedly under the Italian's tenure
Recalling a moment after the crucial draw away to Russia in qualifying, Tardelli said that he knew that the players finally believed in the system.
"On the plane home (after the Russia gam), Richard [Dunne] came over and told us he understood why we have won so much," Tardelli told BBC Sport. "Because we pay attention to every tiny little detail of play."
He continued: "We knew when we took charge [in May 2008] that the Irish players' mentality was like an English mentality and totally different to an Italian player, who prefers to wait rather than trying to make things happen.
"In England, there are more chances and more goals, but we wanted the team to be more tactical, more disciplined and more like the approach in Italy.
"We told them at the start that, if you have that mentality, then it is possible to achieve any result.
"I realised in that moment after the Russia game that they had started to believe us," said the World Cup winner.
And the 57-year-old believes that the Irish fans also shared the mentality of the players, but says that the tactical approach that he and Trapattoni have implemented has reaped rewards.
"The Irish fans have the English mentality too," he said. "But we have achieved a lot by qualifying for the European Championship after 24 years. I am proud of that."
He continued: "Also, we won a trophy last year, the Nations Cup , and the only reason we didn't go to the World Cup was Henry's handball.
"For me, the players have improved since we arrived because we found a team that did not believe in themselves. They had lost 5-2 to Cyprus and they were very down. I think now they believe in themselves again.
"Results are good and when I walk in the street with Giovanni, the fans are happy. And if people are saying we didn't play well then I would answer that by saying if you are not playing well and working together, then you do not get the results we are."
Tardelli also took the opportunity to praise the character of his mentor Trapattoni, who he has known for many years.
"Giovanni is a gentleman, a great professional and a teacher," Tardelli said. "He loves football, he is a passionate guy and he likes to learn more himself."
He added: "He stays on the training pitch for many hours and he watches many DVDs of opponents because he wants to know everything about the other team.
"I have learned so much from him down the years. I disagreed with him sometimes when I was a player, yes. But not now. We speak every moment of the day but we never disagree because I understand football the same way he does," concluded Tardelli.