The Black Cats hardly put up a fight against the bottom of the table Baggies on Saturday as they went down 3-0 at the Hawthorns.
The result leaves the club four points off the drop zone with four games remaining and Quinn is looking for a massive improvement at home to Everton on Sunday.
The Sunderland chief believes his players let the fans down at the weekend but feels the Black Cats faithful will keep backing the side until the end of the season - providing they show they are up for the fight.
"We had a very, very poor game on Saturday," he told Sky Sports News.
"Our fans went home very, very unhappy but prior to that we played two smashing games at home so the players know what they have to do next Sunday against Everton.
"They have a couple of days to lick their wounds but then they will have two or three days to rev their engines up and get going for a game.
"Sunderland fans want one thing, they will forgive anything. I saw them clap their manager for two hours at Maine Road one time many years ago when they got relegated, because he had a team that gave everything.
Genuine passion"Sunderland fans just want to see the team give genuine effort, genuine passion and run until they drop and that's what we have got to do for the next few games. They didn't do that on Saturday but they know they will have to do it next Sunday."
Quinn insists he has not really thought about how many points the team will need if they are to avoid the drop, but he did add that he would breathe easier if the Black Cats reached the magic 40 points total.
"Ideally we would like to be seven points ahead of the team in third last with two games to go," he laughed.
"But I'm not so sure that will happen. We have to aim for that, we have four games left but the reality is anyone who gets to the 40 points will be breathing a much softer sigh.
"That's what we have to do, try and get 40 points and a win on Sunday would really set it up for us."
The former Sunderland striker is also confident that despite his lack of managerial experience, Ricky Sbragia is the right man to keep them up.
"He has been there as a coach and he has been in dressing rooms before so we have no fears about that," he continued.
"Ricky is doing a fine job to get them to play as well as they did against Man United and Hull in the circumstances. We just need a repeat performance of that.
"I genuinely believe in what we have got in terms of talent, if the work rate is good and if we are passionate and making our tackles and with the Sunderland crowd behind us, Ricky and the players will be fine.
"But they have got to deliver and show the people that they want it."
AcknowledgementQuinn went on to wish former manager Roy Keane well in his new post at Ipswich, while also congratulating one-time Sunderland boss Mick McCarthy on his promotion to the Premier League with Wolves.
"A lot of stuff has been said but it's not right being chairman of my club to be talking about other clubs and other managers, but I haven't had the chance to wish him (Keane) well so I'll do that," he added.
"He had a smashing time at our place and will always be fondly remembered and I haven't had the chance to congratulate Mick McCarthy, another Sunderland manager who's doing well. I just need us to do well now."
Meanwhile, the Irishman praised PFA Player of the Year Ryan Giggs, stating that if all professionals were like him his job would be a lot easier.
"I think it's fitting. I was stunned that he hadn't won it before and that kind of sums it up really," he declared.
"The guy is just phenomenal and has done it with a sense of professionalism that's just beyond comprehension.
"You look at all his medals and how he conducts himself, you look at all the work he does in the community.
"If they were all like him then we would all be happy chairman I'll tell you that."