Forest were chasing a club record-equalling seventh straight win but it looked like manager Billy Davies would suffer defeat for the first time in eight games when Will Buckley put the visitors back in front with five minutes left.
Having impressed between the sticks for the Seagulls, Ankergren lost concentration for once in injury time allowing Henri Lansbury's shot to squirm under his body and hand the hosts a point.
Poyet, whose side still climbed into the play-off zone, said: "To begin with I thought the shot must have taken a deflection but when I've seen it again I nearly killed myself!
"When you are a keeper you pay the price and Casper has done that today. He was having a very, very good game, making two or three good saves, coming for crosses and kicking very well.
"And in training he will save a 1,000 shots like that but we wanted him to save it today. Goalkeeper is a terrible position to play but we lose together and we win together - at least we got a point.
"At half-time we didn't look like getting that because we were very poor in the first half. I wasn't happy but we were much better in the second half and had a very good chance to win the game ... and almost did."