Pardew has won just one of his 14 Premier League games in charge since replacing Tony Pulis in November.
Basement side West Brom desperately needed something from the game and looked to be heading for a point until Deeney broke clear after 77 minutes and fired a superb shot past Ben Foster into the roof of the net.
Albion lost 1-0 to Watford on Saturday but deserved to get something out of the game after a committed performance from their players.
"If the consequences from this defeat are that I lose my job then that will be what it is", said Pardew.
"I don't think it will be easier to play against West Brom than to play against Arsenal in the next game (after that)", he said.
The pair exchanged some words after the Premier League loss to Huddersfield last week
"I try to be concentrated on the next match and am focused on the next three points, because we need them", Gracia said. "I'd be foolish and not a good manager if I didn't listen to those comments".
"It is a process of staying true to your profession and that is what I will do and I hope my players do the same", he added. "I thank them for that and I actually feel for them more than myself".
Relegation looks inevitable, with the Baggies last dropping out of the Premier League in 2009, before making an instant return a year later. "It is tough to stand in front of players and say you haven't really done much wrong".
The Baggies board have made a decision to keep the failing head coach in place for at least one more game due to an improved performance against Watford even though Albion lost 1-0.
"It leaves us in a hard position, let's be honest".
"Troy is not only important for goals but important for us on the pitch, off the pitch and he is our captain, too. I want to try and make it function as long as I can".
Deontay Wilder KOs Luis Ortiz to Remain Undefeated, Retains Title
He staggered Ortiz in the ninth before dropping him twice in the 10th, prompting a intervention by referee David Fields . In the fifth, with boos raining down from the crowd of 14,069 at Barclays Center , Wilder finally landed a solid punch.