The two-time champion saw off Adams, who himself has won the World Darts Championship three times, 3-2. Waites spoke to Tungsten Tales after his win, and gave a very frank assessment of the game.
"I played pretty bad - pretty shocking. Martin didn't play much better than me," Scotty 2 Hotty summarised.
"His scoring was better, but his finishing was atrocious tonight!
"It could've been 3-0 to Martin, over in 20 minutes. To be honest, I don't know how I've come off as the winner.
"Grit and determination, that's all it was."
Waites reflected on the draw, which landed him into a tough-looking quarter - the 16th seed will play Wesley Harms after dismissing Adams.
"There's no easy draw when you come into the World Championships. All these players have played all year to get here, and they deserve the chance," he said.
"But to get the three-time champion in the first round - that's the last thing I really want!"
The question of prize money was also asked of Waites, who earned £35,000 as runner-up last year and would earn £50,000 if he goes on to win at the O2 Arena. The Yorkshireman insisted that controversy surrounding funds won't affect his title bid.
"Coming up to a tournament, you can't worry about the prize fund. You've still got to do the same preparation.
"It's just a bit of a kick in the nuts sometimes, that's all it is," explained Waites.
"I don't care if I'm playing for a penny or a pound, or £100,000. I'll still do the same thing."