Zaha scored from the penalty spot at Selhurst Park on Saturday to take his tally for the campaign to four – the same amount of Premier League goals he managed across the whole of last season.
However, that was the only shot on target Palace managed during the entire game before Alexis Mac Allister scored in the 90th minute for the Seagulls.
It was the first game since the closing of the summer transfer window, another in which Zaha failed secure a move away from Palace despite having laid out his ambition to play Champions League football 18 months ago.
Zaha’s performances have been improved this season, but he was too quiet against Brighton.
While not helped by a Palace side pinned so deep in their own half, his own efforts after the penalty were well below the standards many expect from the Ivory Coast international.
During seven minutes of added time when Palace were chasing a winner, Hodgson could be heard bellowing: “Stop talking, Wilf” when the Palace forward became embroiled in a heated argument as the clock ticked down.
Speaking after the game, Hodgson said: “I always think that with a player of his ability, he has got more to offer. We have so much faith in his ability and always feel, with a bit of luck, there’s more there to give.
“What I will be preaching to him for the rest of the season is that a player of your ability has got more to give and it is not sufficient to just score a few more goals than last season.
“I want to see him create havoc in the opponents’ defence and he didn’t really do that today.”