Allardyce has said Silva's record bore no comparison with his own because "he got Hull City relegated last season".
But the ex-Sporting Lisbon and Olympiacos boss, who Everton wanted permission to speak to before appointing the ex-England boss, has suggested he should wait a good few years before his comparison can be valid.
"Go and see what he [Allardyce] was doing when he was 40 years old, or see what he was doing in his first seven seasons as a coach" Silva told The Mirror.
"Then look at what I am doing at the same age - or you can wait until I am 63 years old, and then we can compare what I have done.
"I read what he said, but when he made this comparison it does not make sense.
"It's like me comparing the five goals [Watford forward] Richarlison has scored in the Premier League with [Stoke striker] Peter Crouch.
"Crouch is nearly 37, Richarlison is 20 - Crouch has played so many games and Richarlison far less."