The Czechs went in front against the run of play but Portugal kept their heads and, thanks to an own goal and an added time strike from substitute Francisco Conceicao, managed to take all three points from the Group F match.
"Today we showed heart, yes, but also a lot of discipline, we played and controlled the game and we didn't let Czechia use the goal they scored and this is the most important thing," Martinez told reporters.
"Today we showed incredible value and we showed the strength of all 23 players and the keepers who are here, and I need to thank our fans, the atmosphere they created helped us win this game."
Portugal fell behind in two of their friendlies this year, and went on to lose both games, but against the Czechs, when it really mattered, they found a way to recover and grab the win, thanks also to player of the match Vitinha.
"He was a very important player throughout all the friendlies, on the pitch and off it. We have a very competitive team and its important to have players like Vitinha who can help us control the game," Martinez said.
"We managed to concede, to be one goal down and still win the game. We lost against Slovenia after conceding the first goal, Croatia as well, but today we won."
Porto forward Conceicao came off the bench in the 90th minute and less than two minutes later took full advantage of some poor defending by the Czechs to snatch a late winner.
"Francisco is the ultimate example of earning it, he deserves to be here and he showed he's ready to help the group," Martinez said.
"A very natural player, he's got a nose for danger in the box.
"Francisco is doing what he's been doing over the past four months in his club team, but this is not easy but he showed character and worth because he was allowed to be here."
Portugal dominated, both in terms of possession and chances created, and although they were almost punished by a resilient Czech side, the manager had nothing but praise for his squad.
"Things were tough for us today but we deserved to win, and for a national coach its amazing to have a group of players that's as resilient and as caring as they are," added Martinez.
