Tony Pulis' side beat West Ham 2-1 at the Britannia Stadium on Sunday to set up a semi-final clash with Bolton at Wembley next month.
Before that, Stoke will hope to break a four-game winless run in the league, with their first opportunity coming at home to Newcastle this weekend.
Ecstasy: Danny Higginbotham's free kick creeps over the line to send Stoke into the semi-finals
The Potters go into the game three points above the relegation zone, and Coates told www.stokecityfc.com: 'To get to Wembley is great for us and it's great for the whole area because we haven't been too often in the past.
'Are we dreaming of more cup glory? No, we're not dreamers, we're pragmatists, and I know that Tony Pulis will have nothing on his mind now other than letting three points when we face a big game against Newcastle on Saturday.
'If we can win that game, then it will have been a fantastic week for us because we still need at least six points to make our league position look more comfortable.
'The priority remains to stay in the Premier League and to finish as high in the table as possible.'
Agony: Stoke's poor league form was compounded by the 3-0 defeat to the Hammers
Coates admitted he was hoping for Bolton when the draw was made - leaving a Manchester derby in the other tie - but he knows Owen Coyle's in-form side will provide a stern challenge.
He added: 'When I went into the boardroom after the game, I was asked who I wanted in the draw, and my answer was Bolton. But I imagine that if you'd asked them the same question at Bolton, they would have said Stoke City.
'It's only natural that we would prefer to miss the two Manchester clubs, but Bolton have been made the favourites, and the bookmakers know what they are talking about.
'They have been in the Premier League much longer than us and they're higher in the table at the moment, so it's perhaps not surprising.'
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