Roy Hodgson's charges could not find the decisive goal against the Seagulls in a tight contest at the Falmer Stadium.
And the Cote d’Ivoire international who played the entire duration of the clash has expressed his appreciation to the Eagles’ faithful for their support via his social media page.
“Another step in the right direction. Thanks to the travelling support,” Zaha wrote on Twitter.
Zaha has scored three goals in his last seven games for Crystal Palace.
And the ex-Manchester United winger will be looking to help his side pick up a positive result when the Eagles travel to the Hawthorns to trade tackles with West Bromwich Albion on Saturday.
Roy Hodgson's side, currently bottom of the English Premier League log, will be looking to pick their third win of the season against the Baggies.