Mexico visit Honduras next week still needing one point to make sure of reaching the final round of the CONCACAF region's qualifying competition, which will be played next year.
"I've not at any moment had doubts that Mexico will be at the World Cup in South Africa in 2010," Eriksson was quoted as saying on the Mexican federation's website.
"We knew it would be difficult, but I also thought we could have settled this in Canada or Jamaica. Now, we have to try and book our ticket against Honduras."
Mexico won the first three matches in semi-final Group Two, all at home, but then lost 1-0 in Jamaica and were held 2-2 in Canada. They also lost to Chile in a friendly.
"I feel fine," said the Swede. "We are close to what we want, the match against Honduras is important for everyone in this country, supporters, players, federation, press. I know what it means but I'm not under pressure.
"The standard of Mexican football is high," he added. "It's not the same as the Premier League but it's a very good standard. It's evenly-balanced."
Former England manager Eriksson said that Tottenham forward Giovani dos Santos would not be available to face Honduras on November 19 because of injury.
He was also surprised at recent comments from Cuauhtemoc Blanco, who announced his international retirement in September but has recently said he would be prepared to reconsider.
"I find it a little strange that a player says one day that he doesn't want to play in the national team for a number of reasons, then tells the media that he's available.
"Firstly, you don't change your mind from one day to the next. Secondly, if any player wants to talk to me for any reason, I prefer him to call me or any member of the technical staff rather than send messages through the press."
Mexico face Ecuador in a warm-up friendly on Wednesday.
