The Gunners needed a last-minute penalty from Alexis Sanchez to beat the Clarets, and subsequently climbed into the top four as a result.
Bellerin took to Twitter after the result, saying "some would say we have cojo***!"
The remark appears to be a reference to Deeney's quotes after Watford scored in injury time to beat the Gunners 2-1 in October.
After the match, Deeney claimed that Arsenal lacked the "cojones" for the top-four fight, saying: "I've heard Wenger's already blaming (a penalty decision) as the reason why they lost. I'm not going to be the one to tell Mr Wenger about himself, but there's a reason why they lost and it wasn't because of one penalty.
"I'll have to watch what I say. It's (having) a bit of cojones, a bit of nuts."
Arsenal face Huddersfield on Wednesday, before a marquee match-up with Manchester United.