Oribe Peralta struck in the second half as Mexico overcame the African side 1-0 in heavy rain in Natal.
The win took them joint top of Group A alongside Brazil, who now lie in wait in Fortaleza on Tuesday.
It is a formidable task but Ochoa is full of confidence.
The 28-year-old told FIFA.com: "We're not nervous about it at all.
"In fact, getting a start like this has calmed our nerves. The team's only going to get stronger and we're on the up and up.
"So we'll be going into the game in a happy frame of mind and ready for the challenge."
With another tough game against Croatia also ahead, it was important Mexico started with a victory.
The result proved the very least they deserved, with former Tottenham forward Giovani dos Santos having two goals controversially disallowed for offside.
Mexico were the more enterprising side throughout and their lively front pair of Peralta and Dos Santos justified their selection ahead of Manchester United's Javier Hernandez.
Ochoa, who plays for French club Ajaccio, said: "Our opponents made it a tough game and the conditions made it even harder.
"When you get rain like that it makes life difficult for goalkeepers, but I'm happy with the result."
Ochoa was making his World Cup debut after being an unused squad member in the last two tournaments.
He had little to do throughout the game but produced a good save in injury time to keep out a Benjamin Moukandjo header and preserve the three points.
He said: "I'm pleased I was able to help out my team-mates on the pitch and to have made my debut at last.
"I was alert and luckily I was able to chip in with my save.
"The important thing is that we showed how brave we can be. The team looks pretty strong mentally."
Cameroon did hit the post through former Chelsea striker Samuel Eto'o in the first half and Tottenham's Benoit Assou-Ekotto had a free-kick deflected narrowly wide.
But the Indomitable Lions generally created little and it proved a miserable afternoon for them after a chaotic tournament build-up.
Cameroon's arrival in Brazil was delayed after a row between the players and the national federation over bonuses.
They return to action against Croatia in Manaus on Wednesday and they look to have an uphill struggle to remain in the competition.
Their German coach Volker Finke, however, remains optimistic.
Finke said: "We have five days to recover. We will analyse this together because the match against Croatia is very important if we want to stay alive."