Bowyer, who begins his second spell in temporary charge this season after the departure of Michael Appleton, insists the supporters have a huge part to play between now and the end of the season.
"The main thing for the supporters is to back the team the way they did against Burnley," he told the club's official website.
"They backed the side right until the death and with Dunny scoring in injury-time was great for us and gave us the boost to go into this game.
"With the experience from sampling that atmosphere we want to appeal to the fans to come and cheer the football club and the players on once again.
"Because when the fans are like that the players respond and vice-versa. It is much needed."
He also admitted three points against Paul Ince's side are vital if they are to distance themselves from the bottom three.
He added: "We've got to try and win the game and get the team climbing up the league. You've always to be realistic and we have to try and get some wins as quickly as possible.
"Hopefully we can the start climbing the table. It has been a tough season and we want to finish it on a high now."
Blackburn last week