Brewster was only placed in charge for six games following Steve Evans' departure to Rotherham and admitted he was delighted to take them up.
"It's a great achievement," said Brewster, whose side needed to win their final game at the Crown Ground to secure the third automatic spot in League Two. "I was placed in charge for six games to try and take Crawley straight up and I am just relieved to take them over the line."
He added: "I am proud of the players and they deserve the credit. They have stuck together and come through it.
"It's a small club and it's an amazing achievement to be in League One and achieve back-to-back promotions.
"I heard the scores at half-time and knew Southend were winning so, with it being goalless, I knew we needed a goal.
"Our keeper Scott Shearer made some vital saves in the first half but then we started to get into it. We were dogged and kept going and finally got the goal I thought we deserved."
Stanley assistant Leam Richardson, whose side finished mid-table after being in the play-offs last season, said: "It's never nice to see someone else celebrate on your home ground.
"I wish Crawley all the best and we will be using this moment to hopefully inspire our lads at times next season. It's mine and Paul Cook's first full season in charge next season so there will be changes. We will be looking to put together a team capable of winning promotion.
"Again against Crawley, we didn't take our chances - their keeper was superb in the first half - and that's what has cost us in the last few games. It was a sloppy goal to concede but now we move onto summer and look to emulate Crawley."