Appearing at his fourth World Cup, man-of-the-match Marquez opened the scoring in the 72nd minute, powering home a header from a corner and turned provider 10 minutes later, flicking on for an unmarked Javier Hernandez to head into an empty net.
Andres Guardado had added a second three minutes after the Marquez strike as Croatia chased the victory they needed to qualify.
"Rafa, I called him and asked him to be captain and the leader of our team," an elated Herrera, who took over as Mexico manager in October, said.
"We needed a leader, concentrated, involved, commanding, screaming, shouting, giving my instructions on the field," he said.
"I did not hesitate to appoint him captain. He was the only one, if nothing happened and God-willed and he was in good shape. I had no doubt that he was number one in the list of 23."
"He has given leadership in the group, that's why they call him 'the boss' in the group."
The victory gave Mexico second spot in Group A on seven points with hosts Brazil topping the standings on goal difference following a 4-1 victory over Cameroon.
The Mexicans will face Group B winners the Netherlands in the last 16.
Having gone into the game with doubts about his side's ability to handle Croatia's aerial power, Herrera turned the tables and his team scored two goals with headers from set- pieces.
"In the first half we maybe lacked a little daring play, we were pressured, thinking that with a draw we would qualify," Herrera said.
"At halftime we discussed moving Rafa to the front at set- pieces. Then we were very happy when you see the first goal."
Having seen two efforts cancelled out by poor offside calls against Cameroon, Herrera once again found fault with the officials.
This time, the referee waved away Mexico's appeals for what looked like a certain penalty when Croatia captain Dario Srna appeared to handle the ball in the area.
"We see a lot of mistakes in our matches, the US and Costa Rica haven't had that. It's against Mexico, I'm talking about the games that Mexico have played.
"We are disturbed by the refereeing situation, in two out of three matches it has gone against us. We had two goals disallowed and FIFA has already reacted by sending home the linesman."