In the first leg of the intercontinental FIFA World Cup play-off in Mexico City, the home side blitzed New Zealand to lead 2-0 at half-time and then effectively ended the two-legged tie with three more goals in the second half.
Herbert said after the game that his team had disappointed him with their defending in the air, after he had selected a back five of Leo Bertos, Andrew Durante, Ivan Vicelich, Tommy Smith and Tony Lochhead.
"The defending off crosses, allowing players free in the box at crucial times; we've always been incredibly strong in that area," Herbert told nzfootball.co.nz.
"That's more disappointing for me tonight, the way we conceded the goals."
Mexico left wing-back Miguel Layun regularly found space past Bertos, setting up Oribe Peralta's double in the second half before the home side's captain Rafael Marquez headed in his team's fifth goal with six minutes remaining.
A volley in off the post by Chris James just one minute later saw New Zealand pull a goal back ahead of next week's second leg in Wellington and Herbert argued his team owed it to their fans to not give up despite the four-goal deficit.
"We have a responsibility to return home and give it our best shot; we've got a sold-out stadium in Wellington and it's our duty to turn up and make that as close as we can," the 52-year-old coach said.
"It won't be over until the 90 minutes in Wellington and we'll be incredibly positive in what we do."