The 22-year-old midfielder agreed a new deal, which keeps him at the club until 2017, late last week after an impressive run of form for the Ewood Park outfit.
A graduate of Rovers' youth Academy, Lowe has established himself since making his debut in 2011 and has been an ever-present in the Championship this season.
But with the new contract satisfying both parties, Bowyer has called on the player who captained England at the FIFA Under-20 World Cup in 2011 not to rest on his laurels.
"You can talk to managers up and down the country and they'd all want a Jason Lowe in their team," Bowyer told the Lancashire Telegraph.
"But what he is doing this season is showing he can be more than just one of those unsung heroes. He's bringing more to his game and he's trying to become that old-fashioned midfielder that can do a bit of everything.
"The next stage is to get some goals into him. If he can do that it will make him even better.
"We're not putting a restriction on him just to sit in front of the back four. We want him to get up there and contribute goals as well."
Bowyer has worked with Lowe throughout the player's rise through the club's youth system into the first team and admits it is inevitable that he has attracted interest from elsewhere.
He added: "It goes hand in hand - if you're putting in good performances it alerts other clubs and brings attention."