Burnley knocked Fulham, Chelsea and Arsenal out of the Carling Cup and came within two minutes of overcoming Tottenham in the semi-final second leg.
With one Wembley dream having died, another remains alive and victory over Albion would hand Coyle's side a fifth-round trip to Cardiff or Arsenal.
Coyle, whose reputation has soared since his arrival from St Johnstone in November 2007, said: "We expect a tough game every time we take to the field because people respect us and know about the talent and the ability within our squad.
"It's a game against another Premier League team, which we have thrived on all season.
"I hope that we can replicate the performance we showed at the Hawthorns and come up with a better result.
"Yes, we have played an awful lot of games, but I still want an FA Cup run and try to marry that up with the Championship, which is our bread and butter."
Burnley's small squad have been severely stretched in recent weeks and, while they have prospered in the cups, their Championship form has suffered.
However, Saturday's 2-1 home win over Charlton ended a run of five successive League defeats and gave Coyle and his players a timely lift.
Only eight league positions separate the sides and Coyle is a confirmed admirer of Tony Mowbray.
He added: "I know Tony personally and, aside from being a top football man, he's just a class man himself.
"He's got a very good team and they went to Hull on Saturday and came back twice to draw 2-2.
"But there has been a special atmosphere for the cup ties this season, particularly here at Turf Moor, and we want the fans to create that again tomorrow night."
On-loan Middlesbrough defender Rhys Williams is ineligible and left-back Stephen Jordan remains sidelined due to a knee ligament injury.
West Brom, who lost to eventual winners Portsmouth in last season's semi-finals, have 12 players under treatment. Late fitness decisions have to be taken on central defenders Abdoulaye Meite and Ryan Donk, who both have groin problems, as well as midfielders Borja Valero (hamstring) and Robert Koren (calf).
Albion on Monday signed defensive midfielder Youssouf Mulumbu, 22, on loan from Paris St-Germain until the end of the season with a view to a permanent deal. The Democratic Republic of Congo player is not eligible on Tuesday night but could make his debut against Newcastle on Saturday.