Mathews' breathing was compromised in the fourth round after he broke his nose when the two fighters clashed heads.
Until then, it had been an even contest, with the challenger having the better of the opening two rounds before Rees fought back.
"I'm absolutely devastated, Mathews told Sky Sports News. "I've worked so hard for the fight and I know Gavin has, but things happen in life and you've just got to get on with it."
The two competitors spoke openly about a rematch after the bout, and Rees was hopeful that another meeting would take place in the near future.
"It was building into a good fight to be honest and it's a shame for the fans," said the champion. "I don't know if I've got a mandatory now but if not he can definitely have another shot."
The outcome marked the first time that both boxers had drawn a contest in their professional careers.