Sunday's 2-1 defeat to Burnley, Rovers' first against their bitter rivals in 35 years, had left this part of East Lancashire in desperate need of a quick riposte against former Clarets boss Eddie Howe's Cherries.
However, Lewis Grabban's 15th goal of the season consigned Rovers to a third-straight loss and, with just 12 games remaining, their hopes of bridging a nine-point gap to the Sky Bet Championship play-offs appear to be diminishing by the game.
But Bowyer said: "We've got 12 games left to play in now and until it's mathematically impossible, you keep striving to get as high as you can and hopefully into the play-offs.
"It's important now that we regroup, we stay calm and we stick together. We've worked hard to get stability into this club. These last three games - we've got to make sure we stop that, obviously - but there's no need to panic or anything daft like that."
There was a sombre feel around Ewood Park throughout the game and boos greeted the half-time whistle, so those voices of discontent only grew louder when Grabban rifled home 23 minutes from time.
Asked about the anxiety, Bowyer said: "That was always the concern, but we knew that and understood that and we now have to regroup and get over it quickly."
In a tense game of few chances, the better opportunities feel to the visitors with former England goalkeeper Paul Robinson saving from Matt Ritchie in the first period while Simon Cook nodded against the post from close range.
"We haven't made their goalkeeper work enough," Bowyer admitted.
"That said, I think Paul Robinson's only made one save first half and the lad (Grabban) has had a great strike. Other than that I don't think either goalkeeper was worked."
The victory was Bournemouth's third in a row and they have also recorded a hat-trick of clean sheets in March to move Howe's side one point off Rovers.
They became just the fifth team to win a Championship game at Ewood Park this season and Howe vowed there is more still to come from his youthful side.
Asked if that was their best performance under him, he said: "It's up there, I wouldn't say it's our best.
"I think we've played better than that - at times in the first half we gave the ball away under little pressure and I felt we were close to totally dominating the game first half without ever having the cutting edge that we needed and turning our dominance into goals.
"But we're still building, there's still more to come from this team and I think that's our next challenge."
The next phase of that rebuilding process will surely occur in the second tier next season given the Cherries are in the top half and 16 points clear of the bottom three.
Yet Howe argued: "We've got a lot of games to come, a lot of points to play for.
"If you look at our side tonight you wouldn't think we were going to get involved in a relegation fight but, football being football, you need to get the points, you need to get the wins so we'll continue to keep our feet on the floor but recognise that we're building nicely."