West Bromwich Albion's Salomon Rondon celebrates his goal
The match looked like it was heading for a goalless draw until Venezuelan striker Salomon Rondon got a touch on James McClean's 74th minute free-kick that took the ball past Palace 'keeper Wayne Hennessey.
Palace had dominated the match in terms of possession with 63% in their favour, but the two sides only managed seven shots on target between them.
He added: "It's fair to say we know his heart and soul may be elsewhere."
Alan Pardew looks on as his side fail to trouble the scorers
Pardew is finding himself increasingly under pressure among Palace fans.
The South London side has now lost more games and scored fewer goals than any other side in 2016 with the exception of relegated Aston Villa.
In the aftermath of the opening-day defeat, Palace fans took to Twitter to register their disillusionment with the manager, with #Pardewout being used by some disgruntled fans.
Others elected to focus on Pardew's transfer policy, with many hoping that the manager will sign a new striker before the window closes.
Pardew will need to pull something out of the bag if he is to arrest Palace's declining form and silence the burgeoning social media campaign for his removal.
His team takes on Tottenham next Saturday, and will hope for a repeat of February's FA Cup 5th Round tie when the Eagles defeated Spurs 1-0 at White Hart Lane.