Former England coach Eriksson succeeded Hugo Sanchez in July 2008 with the task of steering Mexico to the 2010 World Cup finals in South Africa, but four wins in nine matches left the team in danger of failing to qualify.
"A bad decision was made to put someone (in charge) who maybe didn't know the country, Mexican football, their players, the environment and who couldn't transmit what Javier (Aguirre) now transmits (to the team)," Marquez told reporters.
Aguirre took over from Eriksson in April and began with a defeat against El Salvador that made Mexico's position in the six-nation final CONCACAF qualifying group even worse.
Four consecutive wins have since put Mexico back on track and they are confident of securing a finals berth when they play their last qualifiers at home to El Salvador on Saturday and away to eliminated Trinidad & Tobago four days later.
"We all doubted (we would qualify) but Javier's arrival has changed the direction of everything, we trust in his work and we must try to carry it through," said Marquez, back in the team after two months out with injury.
Mexico are second in the group with 15 points, one less than the U.S., with Honduras on 13, Costa Rica 12, El Salvador eight and the Trinidadians five.
The top three qualify while the fourth-placed team play off over two legs against the side finishing fifth in South America.
