After a remarkable weekend in the battle to avoid relegation, Sunderland go into the game in the knowledge that if they beat Everton they can secure their status in the top flight for another season - and relegate Norwich City and Newcastle United in the process.
Allardyce is quoted in the Sunderland Echo, saying: "There’s this air of ‘surely we’ll beat Everton after beating Chelsea’.
“That’s not the case. We’ve got to perform at the highest level because Everton will come having been criticised for their performance against Leicester.
“Roberto (Martinez, Everton manager) will have them really fired up to give a performance and we have to be very careful about an Everton side who have a better away record than home one.
“Because we switched off defensively at Everton, we ended up losing 6-2 there, so they can hurt us with the quality of players they’ve got in the front line."
Everton have been on a very poor run of late and the pressure has mounted on their manager Roberto Martinez, with speculation that he could well be presiding over his final couple of games in charge of the Toffees.
They have only managed the one win in their last nine league games, which leaves them in 12th place in the Premier League, and having been knocked out of both domestic cup competitions at the semi-final stage there is no silverware to show for the side's efforts this season.
Allardyce is right to warn against complacency and he will want to avenge the heavy defeat that the Toffees inflicted on them earlier on in the season. But with such an air of disappointment surrounding Everton's campaign, it is hard to think that Sunderland side do not have a good chance of securing their safety tomorrow night.