Allardyce was left wondering how Sunderland, who are third-bottom in the table with seven games to play, had contrived not to win the game.
"I need to go back to church and start praying," the manager told the BBC. "I can't ever imagine in my long career dominating a game for so long, creating so many chances and not winning it.
"It's a cruel blow on the basis of the position that we're in... in such desperate need that we are for points.
Allardyce was, however, encouraged by the performance and is hoping that Sunderland can replicate the effort they showed against the Baggies and get a win when they host the league leaders.
"It's the best performance we've had since I've been here," he added. "I want us to beat Leicester next week. Let's go and upset the applecart, hopefully play like this and beat them."
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
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