Palacios watched on from the bench as his side slumped to a 3-0 FIFA World Cup defeat against France last week, a result that leaves their last-16 hopes hanging by a thread.
But the 32-year-old is confident of a response from Honduras as they aim for victory against their former coach Reinaldo Rueda.
"We are committed to the country," Palacios is quoted as saying on CONCACAF's official website.
"Many people expect that we will win and play well. The truth is that the group is very strong.
"We know that we have possibilities. Six points are still up for grabs. The match against Ecuador is going to be very important.
"We are in a World Cup where all the matches are finals and we ask the people that they keep supporting us and having confidence in us.
"We know that we can give more and against Ecuador we are going to show it."
Ecuador also lost their World Cup opener as Haris Seferovic's stoppage-time winner gave Switzerland a 2-1 triumph.
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