The 61-year-old dismissed any suggestion he would struggle to meet higher expectations, saying pressure was for "cookers" and he was not afraid of challenges because he had four dogs.
Santos was initially appointed in September 2014 with Portugal at a low ebb and led them through the Euro 2016 qualifiers with seven straight wins, all by single-goal margins.
At the finals, Portugal scraped through their group with three draws before beating Croatia in extra time, Poland on penalties, Wales in 90 minutes and hosts France 1-0 in extra time in the final thanks to a strike by Eder.
Still unbeaten after 14 competitive games with Portugal, the former Greece coach said as soon as they returned home from the finals, he agreed to meet Portuguese federation president Fernando Gomes in the Algarve where they were both on holiday.
"That's what we did after a turbulent, tiring week of unleashing emotions," he said. "We sat down, had a coffee and easily reached an agreement."
"We have a key word which is 'winning' and I promise to fight a lot for this," he added.
"Fear? If I was afraid, I wouldn't be here. In any case, I have four dogs at home. It's not part of my dictionary.
"Pressure? That's for cookers. I'm too old to worry about that. What I have is an obligation to do my work well."
Santos said throughout Euro 2016 that he expected to return to Portugal on July 11, the day after the final, and be welcomed with a party.
He maintained his stance even after a 0-0 draw with Austria in their second game which left them struggling to make the round of 16.
"At that stage, some people were wobbling but the president (Gomes) didn't wobble," he said. "He told me to remember that he was counting on me for the next four years."
"We had just drawn our first two games and a lot of people were asking questions. That had a big effect on me."
Portugal begin their World Cup qualifying campaign with a mach away to Switzerland on Sept. 6. Their group also includes Andorra, Hungary, Faroe Islands and Latvia.
(Writing by Brian Homewood; editing by Ken Ferris)
