The victory, sealed in a finish Martínez admitted was not for the faint-hearted, means Portugal now meet Spain on 6 July, kicking off at 20:00.
"World Cups have this, they're no longer group stage games," Martínez said. "The first half was fantastic. The intensity, the arrival in the final third.
"There's always danger against a team like Croatia, who have a lot of ability to use the ball. Conceding a goal and continuing to believe strongly, using the players on the bench, that's the mentality that helps win games. Perfect games at World Cups don't exist anymore.
"The discipline, the ability to have talent, but then the ability to play with heart."
Martínez said the win carried personal significance for the squad.
"Our players enjoyed it for Portugal, for Ricardo Carvalho's father and for our Diogo Jota and André," he said. "It was Diogo's typical game. 2-1, which is the number 21, against Croatia, who were the last side he scored against, at the Jamor. Many signs. Diogo sent a lot of strength and energy. Now he's very happy and proud."
The coach also addressed his squad depth heading into the knockout rounds.
"We have many different profiles," Martínez said. "There isn't a player at the World Cup who can take a penalty like Cristiano did, and there isn't another striker with the strength and ability to get into the box like Gonçalo Ramos. We had more players who could help. Gonçalo getting into the starting eleven? That's what we want. There are many players, João Félix is also having a very good World Cup."
Cristiano Ronaldo was named FIFA Player of the Match and reflected on a difficult second half.
"Today we had to know how to suffer," Ronaldo said. "To win a competition of this magnitude, we have to know how to suffer. It was a very interesting game for the spectators. We controlled the game quite a bit in the first half, the second was more chaotic. They scored, we went into a bit of stress, but the emotional release came when we scored the penalty. From there, the game was easier. We still had some difficulties, but that's what the competition is, and it's about continuing."
After the match, Ronaldo wore a shirt bearing Diogo Jota's number 21, a year to the day since the former Liverpool and Portugal forward's death on 3 July.
"It's a special day, for our Jota, who is up there lighting our way," an emotional Ronaldo said. "We know he's present with us and it only made sense to win today to honour him in the best way."
Ronaldo also described his farewell to Croatia's Luka Modrić.
"I said goodbye, yes," Ronaldo said. "He continues to be a legend of football, we're almost the same age. I respect Modrić a lot, for what he continues to do in football."