The Latin American side, coached by former England manager Sven-Goran Eriksson, need a point in Honduras on November 19 to reach the final round from CONCACAF Group Two.
"We are in first place in the group, but just by a hair and that's not comfortable," Compean told guests at a soccer symposium in downtown Los Angeles on Monday.
"We did not think it would be so much of a struggle in the qualification rounds.
"We have not got enough points as a visiting team and we have not got the goals we have wanted. We are concerned because our expectations were to be already qualified.
"But we see light at the end of the tunnel. We are certain that we will advance to the next round."
Mexico suffered a shock 1-0 defeat in Jamaica last month before being held 2-2 by Canada.
Mexico, who could have qualified with a win in Jamaica, lead the group with 10 points, one ahead of Honduras and three clear of the Reggae Boyz.
They have failed to win away from home in three attempts under Swede Eriksson, once in a friendly and twice in the qualifiers, giving more ammunition to critics who said he was not ready for the tough conditions in Central America.
"Eriksson was hired to do something beyond what we were already doing," Compean said.
"He has been successful in Europe in countries where soccer is competitive -- Italy and Portugal -- and he has twice taken England to the World Cup quarter-finals.
"He has already come up with great ideas and he has accepted the challenge with a great degree of professionalism and a desire to work 100 percent. However, the most important thing is the results."
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