The visiting Wanderers rode their luck as Gus Poyet's Albion struck the woodwork no less than three times and also saw an Ashley Barnes spot-kick saved by Adam Bogdan.
Bruno Saltor eventually seized the lead for the hosts with a sweet volley, but Freedman's side snared a point at the death when David Ngog struck deep into injury time.
Freedman said afterwards: "Brighton were fantastic. I have seen them many times and this was certainly one of the best performances. They will be gutted not to have won.
"When you have one chance, as the one that came our way, you need to take it and David Ngog made no mistake.
"It was all about the character and determination that we showed. We didn't give up."
On suspicion of a handball in the lead-up to Brighton's opener, Freedman added: "I can't blame the referee. He has to turn up and referee on a part-time basis and is trying his best.
"Until we have a situation when there's professional mentoring I can't say a bad word. It's so pleasing that we are becoming a harder side to beat."