Jeremy Payne scored in the 104th minute of play, capturing a crossing pass from Joshua Wood in stride and kicking it to the left side of the net past a diving Mike Randall (Cherry Hill East).
"At least we lost on a good goal," Scarlet Raptors coach Tim Oswald said.
Scarlet Raptors players fell to the Toyota Field turf after Payne's goal, remaining there minutes after the game as the Falcons celebrated around them.
As they did in defeating Loras, 3-2, on Friday night, Rutgers-Camden was able to score a late goal against Messiah (22-1-1) to force overtime.
"The final was a battle, that's the way it's supposed to be in the final," Oswald said. "Two great programs, two great teams all playing for one goal.
"Unfortunately, we came up just short of that goal, but I'm proud of the kids for the season that we had. We chased the whole game, we got a tie, went into overtime a bit tired after playing Loras [in overtime]. We didn't do enough in overtime, and at the end, Messiah beat us with a great goal."
Rutgers-Camden's Taylor McGrory (Sterling) tied the game with 11 minutes remaining in regulation, faking West into diving at his feet, before dribbling around the goalkeeper to score on an open net.
"I played the miss on the ball, it fell right to me, I pirouetted, and I kind of blacked out about what happened [after that]," said McGrory, who scored his season's only two goals during the Final Four.
Randall and Messiah keeper Brandon West were repeatedly tested in the first overtime.
Jack Thompson's kick from 10 feet out for Messiah hit outside on the left side of the net, and two shots inside eight feet were deflected by defenders at the point of impact.
Randall finished with seven saves against the Falcons, who had 18 total shots.