A goal in each half from Scott Dann and Connor Wickham gave Alan Pardew’s side a comfortable second-round victory in south London.
Bowyer had said he wanted Palace to field as strong a side as possible and got what he wished for.
Their starting XI cost around £80m and included debutant striker Christian Benteke.
Bowyer said: “When the (Palace) teamsheet came through, I don’t think it was too much of a surprise.
“It was an opportunity to pit ourselves against the best – 20-odd minutes in and we weren’t doing too badly containing them.
“We knew they would have a hell of a lot of the ball, so we had a bit of a game-plan and you saw signs of that.”
That plan involved a change of formation as Bowyer made four changes from Saturday’s goalless home draw with Wycombe.
In came Will Aimson, Eddie Nolan, Michael Cain and Armand Gnanduillet as the Seasiders opted to play a back five and try to frustrate their hosts.
It worked to an extent in the opening period as Palace had plenty of possession before Dann gave them the lead with a deflected effort on 25 minutes.
The goal briefly silenced Selhurst Park as the ball looked to have hit the side-netting. Seconds later, it dawned on the crowd that it was actually in the back of the net.
Benteke came close to marking his debut with a goal before being replaced at half-time as he tries to establish full fitness following his move from Liverpool last week.
It was his replacement Wickham who doubled Palace’s advantage early in the second half, seconds after Pool keeper Sam Slocombe had saved a Jordon Mutch shot.
Bowyer added: “The two goals we conceded were disappointing.
“The first was a deflection and the second was when we’d just started the second half. We have to manage the game better.
“I wish the first goal had hit the side-netting but we should have defended that a little bit better.
“Then you have the quality of Scott Dann and the deflection wasn’t kind to us.
“The thing to learn from our point of view is you can’t be inviting pressure like we did at the start of the second half.
“We worked very hard and had a right good go together. Those are the qualities you need in the league we’re in this year.
“It’s all about learning and the main focus now is about recovering and preparing for Plymouth on Saturday.”