The Spurs duo are the two most valuable English players around after emerging as some of Europe's best footballers in recent years.
The Tottenham stars are worth an obscene amount of money but Allardyce feels that the masses will be quick to turn against them as soon as they hit a rough patch.
The ex-Sunderland manager points to Wayne Rooney's situation at Everton as evidence.
Rooney returned to Everton in the summer after 13 years at Manchester United and has arguably been scapegoated for the Toffees' sluggish form as of late.
The 31-year-old has three goals in eight games for Ronald Koeman's side, and Allardyce feels he has a "huge amount" to offer in spite of the criticism.
"It’s an epidemic in our country that we unfortunately turn against these great talents – at the moment, Kane and Alli get a lot of praise, but as soon as their form drops, people will turn against them," he told Paddy Power.
"It’s happening to Wayne Rooney now that he is moving into the later stages of his career, and isn’t as good as he used to be. But he still has a huge amount to offer in his experience and as a footballer at Everton.
"Because the club are struggling, people are associating that with Rooney. But I think he’s started well there, he’s scored a few goals, and he’s contributed while on the pitch. It’s unfair on him."