Jordan Rhodes netted the winner for the hosts in the 36th minute to the delight of the home fans in the 15,317 crowd.
"It was a fantastic effort from everybody," said Bowyer, whose side are now two points above the drop zone.
"The supporters were magnificent. I've not heard Ewood like that for a long time. We needed their support
"We've been attacked in the press all season for reasons that the fans and the players can't control so we've developed a siege mentality over the last couple of weeks and we asked the fans to be part of that.
"It's been a team effort but we aren't going to get carried away.
"We've just got to stay calm, we've got to stay positive because there's a lot more football to be played."
Bowyer also praised Rhodes, adding: "You saw why West Ham and other Premier League teams are linked with him and long may they continue to be linked in the press from now until the end of the season.
"We've got to make sure we keep him fit and keep him on the pitch. He's got a big part to play between now and the end of the season, as has everybody."