Despite the long tradition of the Cup, Baggies boss Mowbray insists his only focus is on the league - with promotion to the top flight meaning more to his side than a trip to the Wembley final.
"We're striving for the Premier League, that's our main target and let's hope the FA Cup doesn't get in the way," he told the Birmingham Mail.
"Our league games are our priority. I'm not being controversial but our goal has to be the Premier League."
Sheffield United will get the chance to claim another Premier League scalp when they host Middlesbrough, Blades boss Bryan Robson's former club, Barnsley will travel to meet Liverpool and Preston will face Portsmouth at Deepdale.
Southampton will hope to avoid an upset when they go to League One side Bristol Rovers.
Manchester United will host Arsenal in the only all-Premier League tie, while holders Chelsea have an apparently comfortable tie against League One outfit Huddersfield at Stamford Bridge.