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.
"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. It was hard with four minutes of injury time but we saw it through and I am just delighted. It's not the time to think about my future, it's time to celebrate."