Herbert's eight-year tenure ended with a 4-2 defeat in the second leg of their play-off against Mexico in Wellington.
Mexico had all-but sealed their passage to Brazil with a 5-1 victory in the first leg and Oribe Peralta's first-half hat-trick at the Westpac Stadium put them out of sight.
He said: "Pay a massive tribute to the Mexican team, enjoy Brazil,
"You've deserved it; you've been the better team across both ties."
He added: "We're very thankful for a superb turn out (at the Westpac Stadium). I’m going to wake up in the morning and think the game is in an incredibly healthy position.
"A very inexperienced team showed some wonderful potential and showed a great deal of appetite against a side (Mexico) where you can make very good comparisons.
"The last 45 minutes was incredibly refreshing. I'll walk away and be incredibly proud of it."
