"Let's put it this way," Allardyce, who has managed six other Premier League clubs, told reporters. "If you look at my track record, why wouldn't I be here irrespective of Marco Silva?
"I have every respect for Marco Silva and I am not criticising Marco Silva but his track record has got no comparison whatsoever with mine. He got Hull City relegated (last season)."
Silva began his managerial career with Portuguese side Estoril and led them to promotion to the top flight before lifting the Portuguese Cup with Sporting Lisbon in 2015.
The 40-year-old, who took charge of Hull last season when they were bottom of the table, said it made little sense to compare his track record with the 63-year-old Allardyce.
"When he (Allardyce) made this comparison it does not make sense. It is the same thing if I compare his work with a national team coach like Gareth Southgate," Silva said.
"If you want easy work, go and see what he was doing when he was 40 years old or what he was doing in his first seven seasons as a coach. Or you can wait until I am 63 years old and we can compare what I have done. That is the best solution."
Silva guided Watford to a 1-1 draw with Tottenham Hotspur on Saturday to keep them eighth in the table while Allardyce's Everton moved up to 10th with a 2-0 win over Huddersfield Town.
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
