The Seasiders wasted numerous chances and only managed to convert three of their 23 shots at goal against an inexperienced and youthful Orient side, who had already been relegated to non-league.
But the win, which was never really in doubt, means Pool will take on Luton Town in their two-legged play-off tie, with the first game taking place at Bloomfield Road on Sunday, May 14.
Bowyer said: “I was pleased with the professionalism we showed but I was disappointed we didn’t convert the number of chances we created, especially in the second half.
“I always want more, I always want better and we should have had better and we should have had more.
“But it gives us something to work on in the week leading up to the Luton game."
Pool eased to a 2-0 lead at half time thanks to goals from Neil Danns and Mark Cullen.
The visitors had briefly threatened an unlikely comeback when Jens Janse reduced arrears but Andy Taylor soon restored the two-goal lead to ensure the three points went Pool's way.
Bowyer added: “For the first goal, it was a fantastic ball from Jack Payne who has been terrific for us for a number of months now.
“He’s got some great ability and he’s put in a great ball but it’s a great header from (Neil) Dannsy too.
"Cullen has got a target he’s set himself so he’s working hard to reach that. I thought it was a fabulous finish from him for his goal but again, he could have had a couple more.
“For Orient's goal I think there was a foul on Brad (Potts) in the lead up but they’ve attacked and I think there was a slip before they got in.
“You’ve got to be ready for those but once they scored I was pleased with how we went about it. We showed great composure.”