But Gayle said the players had quickly forgiven Dyson.
"He was looking in the wrong column. He explained it to us and apologised for that mistake," he added.
"No one wants to make this sort of mistake and I'm not going to kill him or anything like that. There is no reason to point any fingers at this point in time. We're here as a team and we'll go down as a team."
Gayle, meanwhile, refused to be drawn on whether the West Indies would support strike action over a cash dispute between domestic players and their cricket board which could threaten the rest of the series.
Players refused to compete in the three scheduled matches in the board's regional four-day competition in protest at money allegedly owed to them.
The strike followed the resignation of Dinanath Ramnarine, who heads the players' association, as a director of the board.
Gayle's team-mates showed their solidarity by not attending a promotional event by sponsor Digicel earlier this week, while they blocked out the company's logo on the left arm of their shirts with tape for the one-day international against England.
But Gayle said: "The players have no argument with Digicel but we wanted to send a statement.
"We support [the players] in whatever stance they take. The union represent us so we have to stand by them."
And asked if the West Indies players could also take strike action to scupper the international series, Gayle said: "There are talks going on."
England skipper Strauss said that it would be wrong for him to comment on the dispute.
Stauss' side's one-run win came on the back of half-centuries for man-of-the-match Paul Collingwood (69) and Owais Shah (62) as England, batting first on a slow pitch, hit a decent 270-7.
Stuart Broad was the pick of England's bowlers, leading the attack with distinction to take three wickets before Dyson's error handed Strauss his first win since being handed the captaincy in January.
"We definitely needed a win," Strauss added. "We've been working hard but you can only work so long without a victory before it takes its toll."
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