The 23-stone reserve shot-stopper, who is also Sutton's goalkeeping coach, was pictured chomping into a pie during the second half of Monday's 2-0 defeat after the hosts had made all three substitutions.
Shaw’s pie-eating did not go down well with his manager Paul Doswell who admitted after the match it did not show the club in the best light.
Sun Bets had offered odds of 8-1 on Shaw to eat a pie "live on air", with Sutton having already come in for criticism from some quarters for allowing the tabloid to sponsor the match.
The club could now face further scrutiny after Shaw admitted he was well aware of the bet before the game.
“A few of the lads said to me earlier on: 'What is going on with the 8-1 about eating a pie? I said: 'I don't know, I've eaten nothing all day, so I might give it a go later on,'” he told The Independent.
“As I say what is that, Sun Bets had us at 8-1 to eat a pie. I thought I would give them a bit of banter and let's do it. All the subs were on and we were 2-0 down.”
There's debate over whether Shaw could be in breach of FA rules on gambling, but he insists that neither he nor his team-mates had placed a bet.
“I think there were a few people [who placed a bet]. Obviously we [Sutton United] are not allowed to bet. I think a few of the mates and a few of the fans,” he added.
“It was just a bit of banter for them. It is something to make the occasion as well and you can look back and say it was part of it and we got our ticket money back.”
Goals from Lucas Perez and Theo Walcott ended Sutton’s hopes with the Gunners now set to face another non-league club, Lincoln, in the quarter-finals.