Allardyce has questioned the sense of Reid's call-up by New Zealand for their internationals with Tahiti over the past week.
The defender did little more than cheer on his team-mates in New Zealand after making the 24-hour journey with a back injury he sustained earlier this month. Reid remains in doubt for West Ham's Barclays Premier League fixture with Southampton this weekend, much to Allardyce's frustration.
"I don't see any sense in calling them over and particularly that far, because they are injured. I don't see any sense it in at all," he said. "I also think there was an underlining factor that they didn't trust him or us that he was injured."
He added: "There's another underlining factor that tells me that the players are brought there and then they're put under enormous pressure to play, because of the loyalties to the country by the coaches and certain political elements which they have to resist."