Mexico prevailed with goals from Julian Quinones and Raul Jimenez in a match they finished with 10 men after captain Cesar Montes was sent off, though they were rarely troubled.
It was their first victory in the tournament's opening match after seven previous failures.
"This was an emotionally difficult match because we don't experience something like this many times in life," Lira, who provided an assist, told reporters.
"It was a complicated moment, but we all worked on the mental side so it wouldn't affect us and so we could do our job as well as possible."
The match, which featured three dismissals, set a record for the most red cards in an opening game at a World Cup.
"It was important to get the three points and luckily we managed to do that," Lira said.
"Now we have to make sure everyone is at 100% to prepare for the second match and get the three points again.
"The sky is the limit. We're not going to settle for anything."
Mexico next face South Korea in Group A on Thursday.
