The Seagulls created far more chances than their visitors - striking the woodwork three times and missing a penalty when Ashley Barnes saw a first-half spot-kick saved by Adam Bogdan.
Defender Bruno Saltor finally volleyed the hosts into a deserved lead and they looked set to pocket all three points before a last-gasp David Ngog strike ensured honours ended even.
But Poyet said afterwards: "I don't think there is a manager in the whole world who can be upset with the players. We are not getting the credit we deserve.
"There is no other team who can play the way we did against Bolton and yet it finished 1-1. It's up to a crowd of 26,000 to tell the rest of the country that we were unbelievable.
"I didn't think that an equaliser was coming, and don't want to complain about there being 20 or 30 seconds more added-time.
"I am proud and absolutely delighted with what we have done. We were so superior, it's incredible the way we played."