A deflected first half goal from Kevin Mirallas and a second half brace from Nikica Jelavic put the visitors firmly in control in Rovers' final pre-season friendly.
Scott Dann grabbed a consolation goal three minutes from time as Rovers ended their preparations with a defeat for the first time, with the Rovers boss happy with how the team went about their business.
"I've said all along that the results haven't been of paramount importance, for pre-season it has been all about minutes," Bowyer told Rovers Player
"I thought today's game was a great way for us to test ourselves against what is going to be a competitive Everton team. I know Roberto has promised their fans Champions League football and on that showing you can see that they are going to be very close. I thought they were excellent.
"For half an hour I in the first half I thought our shape was very decent and that was the point of the exercise. If we could be organised and disciplined in our shape against a top team like that then it holds us in good stead for the forthcoming season.
"I thought we had three good chances in the first half from Chris Taylor, Jason Lowe and Grant Hanley, so we might have nicked a goal there.
"Overall we are pleased with how they have gone about it in terms of their fitness levels. We know that we have got a lot of work to do in terms of readdressing the squad, but I was pleased with how we went about it.
"Next Sunday is the main thing, the next 46 games that we play in the league, not what has happened in pre-season."