Allen later described his opponent as "devastating" and acknowledged that the performance from the world No.1 player surpassed even Ronnie O'Sullivan, the reigning champion.
Robertson's victory has taken him into the quarter-finals of the contest at the Crucible, where he will meet Judd Trump this afternoon. However, Allen - ranked No.14 in the world - does not think that there are any players on the tour who will be able to stop Robertson in Sheffield.
"I just can't see it; if Neil plays like that, no-one can come close to him - not even Ronnie," said Allen. "He was devastating and Ronnie's never done that to me. I can't see anyone getting close to Neil if he keeps performing like that. He was just devastating.
"He played very well in his first match against Robbie Williams but, and I'm not being big-headed when I say this, to do that against one of the top players in the world like me really does send a message to Ronnie.
"I know I played a few bad safeties and left him a few easy starters, but he was nearly clearing the table. Sometimes you have to hold your hand up and admit you got completely outplayed."
Robertson had started the day with only a slender 9-7 lead but cruised to victory; the Australian won the final four frames in a little over an hour after scoring breaks of 59, 69, 94 and 92. "No-one can touch him if he plays like that, that's as good as I've seen," Allen added.
The world No.1 might have been even more impressive too as he closed in a record of 100 centuries for the season. However, the 2010 world champion missed a black off its spot in the penultimate frame and then missed a red on his 92 run in the decider, but Robertson would not be concerned unduly. "I was faultless. I felt like a cricketer on 99 not out when I was going for that 100th century and I had my celebration all worked out.
"I was going to look up at Stephen Hendry in the commentary box and then missed the final black, and then missed another chance in the last frame. I've got another match to make the record."
Dominic Dale eased to a 13-4 victory over Michael Wasley to secure his quarter-final place, meanwhile. The Welshman will face Barry Hawkins.
Shaun Murphy also booked his place in the last eight with a 13-8 win over Hong Kong's Marco Fu.