Terry was portrayed as a villain after his media outburst on Sunday.
"The reaction I saw from the players at the final whistle yesterday did not suggest this is a squad in danger of being ripped apart by cliques or individuals; if factionalism was king, England would now be heading home," Neville told the Liverpool Echo after England's defeat of Slovenia.
"Much was made of John Terry's press conference in the build-up to the showdown with Slovenia and people are right to say that he was hung out to dry - but not by any of his team-mates.
"When things go wrong for England, certain elements of the Press take great delight in spinning things out of perspective and I genuinely believe John's comments were taken out of context to create a storm.
"Just as there will be some publications that go too far the other way now and claim that England will win the World Cup, it looks like they were waiting for someone to put a foot out of line and then seize upon it.
"John had gone out to give a rallying cry and, perhaps, he was a bit too caught up in the moment. But to suggest he was trying to stage a coup, to my mind, is wide of the mark - all he wants to do is win for England, as his efforts against Slovenia showed."