Criticism of West Indies by former England players has been "borderline disrespectful", says West Indies Cricket chief executive Johnny Grave.
West Indies bowled England out for 77 to set up a 381-run win inside four days in the first Test in Barbados.
Ex-all-rounder Andrew Flintoff said the "world's gone mad" after West Indies captain Jason Holder made 202 not out.
Former batsman Geoffrey Boycott described the hosts before the series as "very ordinary, average cricketers".
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West Indies are above only Bangladesh and Zimbabwe in the International Cricket Council (ICC) rankings.
Speaking before West Indies completed victory at the Kensington Oval, Grave said negative comments about a side who now lead 1-0 lead in the three-Test series were "completely unwarranted".
He told BBC Sport: "Criticism of our players and suggestions that they're not world class is unfair.
"They are so dedicated. We've got 11 cricketers here and many more in the region who want to play Test cricket."
England failed to take a wicket on day three as Holder and Shane Dowrich, who scored an unbeaten 116, helped West Indies declare on 415-6.
Grave added: "I saw Andrew Flintoff say he can't believe Jason Holder got a double hundred, yet I think Jason Holder is a fantastic cricketer and has been performing so fantastically over the last 18 months - a brilliant captain."
Flintoff, 41, averaged 31.77 with the bat and 32.78 with the ball in his 79-Test career, while Holder is currently averaging 33.86 with the bat and 28.29 with the ball in 36 matches.
Holder, who was named man of the match, told BBC Sport after the game: "We were in a good position to win the series from the very beginning.
"We know what to expect from England - they are a quality side - but we have seen some loopholes in their performance in this game and in the past we have seen it too.
"They are beatable - we showed that today. It is a matter for us to keep believing and, if we continue in this vein, there's no doubt we can win the series."
Holder's performance - he also took two first-innings wickets - took him to the top of the International Cricket Council's Test rankings for all-rounders.
England turned down first-class warm-up match
England, third in the ICC rankings, have won only one series in the Caribbean in the past 51 years.
They lost 1-0 in 2009 after being bowled out for 51 in the first Test and drew 1-1 on their most recent tour in 2015, against a side described as "mediocre" by England and Wales Cricket Board chairman Colin Graves.
Before this series, England chose not to play a first-class match. Instead they drew two two-day games against a West Indies Cricket President's XI in which players were allowed to bat twice in an innings.
BBC cricket correspondent Jonathan Agnew said "a lack of adequate preparation" was one of the main reasons why they were bowled out so cheaply at the Kensington Oval on Thursday.
Grave, who was appointed in 2017, said: "We wanted to play a first-class game and asked England to do so.
"We had to pull our best 12 players outside of this team out of our championship to see how our A team would perform against this England side.
"I'd much rather people credit our team. I'd like to see English fans enjoying and celebrating 11 West Indians performing to such a high standard."
The second Test in Antigua starts on Thursday.