Ireland took a fortunate 2-1 win over Kazakhstan on Friday night thanks to two goals in the last three minutes, but winger James McClean vented his frustration at being left on the bench on his Twitter account after the game.
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"Everyone respects the manager and there is no other scenario," Doyle told reporters.
"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."
Doyle scored the winner for the Irish in the 89th minute after coming on as a substitute, and admits the team have to improve in time for their next qualifier against favourites Germany.
He added: "Obviously that will be a big step up in terms of the opposition so we will have to improve a lot. It will be a totally different game."
Ireland face Oman in a friendly on Tuesday night, with Trapattoni expected to speak to McClean about his outburst and then decide whether to keep him in the squad.
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