In their opening Group A fixture in a sodden Natal on Friday, Cameroon could have conceded twice to Giovani dos Santos in the first half, only for the linesman's flag to controversially rule out the Mexican's effort on both occasions.
Mexico eventually hit the front just after the hour mark, Oribe Peralta tucking home the rebound after Dos Santos had seen his initial effort parried by Charles Itandje.
Cameroon were unable to find an equaliser as they slipped to defeat, and Finke was frank in his assessment of his side's showing.
"The conditions weren't an excuse for our performance," he said.
"We had some problems through the middle of midfield in the first 20 minutes or so, but we eventually adapted.
"The second half we were better, but overall we're disappointed.
"We had a few chances to score, and didn't. They had goals ruled out, but that's the way it is.
"Now we've got five days before our next match, which will already be decisive for our World Cup."
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