The hosts dominated the fifth-round tie after falling behind, Joshua King grabbing a hat-trick against a visiting side who were reduced to 10 men following Geoff Cameron's dismissal on the stroke of half-time.
And Bowyer heaped praise on his squad, insisting that the convincing win was no more than they deserved.
"For myself and the players I think it is probably our biggest achievement in the time that I have been in charge," he said.
"The lads are buzzing, they are delighted and rightly so – it was a real Cup tie.
"Full praise to them and full credit to them, they deserve every plaudit going.
"Against a quality team the lads worked ever so hard. It is a great example for them in what you can achieve when you do that."
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