Poyet's men found themselves 2-0 behind after their former loanee Chris Wood had bagged a brace but the manager brought Kazenga LuaLua on six minutes before half-time and the sub scored a superb second-half goal before a David Lopez penalty two minutes from time earned the hosts a point.
"For the first time as a manager I made a substitution in the first half, and it was a proper fightback," said Poyet.
"There was desire, character and belief. It was all one-way and a great football comeback.
"We didn't give up, we went for it and, for a moment, I thought we were going to win it, but we are satisfied with a point.
"We've seen a massive change in Kazenga. He is totally different now and is training well and desperate to play."
Wood is now on loan with Millwall from West Brom and he impressed Poyet with his display.
"He is the kind of player we would like to bring in," said the Brighton boss.
"He's only 21 and I feel he will be a top, top player. When he was with us on loan he was a baby but now he is maturing. He's a man now.
"He's clinical and brave and we have played a part in helping him on his way."