McClean was an unused substitute in Ireland's 2-1 comeback victory over Kazakhstan in their 2014 World Cup qualifier on Friday and was not pleased with it.
"Everyone respects the manager (Giovanni Trapattoni) and there is no other scenario," Doyle is quoted as saying by Sky Sports.
"The atmosphere is the same here as it has been in any Republic squad I've been involved in.
"Everyone is entitled to their opinion, but as far as I can see everyone is right behind the manager and hopefully that win will help ease the pressure on us."
Ireland are back in action on Tuesday when they take on Oman in a friendly international in London.