West Brom had won just seven of their opening 25 Premier League games which resulted in the club relieving manager Roberto Di Matteo of his duties in January.
The Baggies have seen an improvement in their form since former Liverpool boss Roy Hodgson took over, remaining unbeaten in the league, and currently sitting in 13th position.
And defender Shorey is confident that West Brom can match their relegation rivals and stay in the English top flight, but will need to focus on each game individually.
“We have got a tough run-in but I think whether you’re playing the top teams or the teams about you it’s going to be a tough game,” Shorey told Absolute Radio.
“We look at our run-in and we have got some fixtures where you think ‘Oh my God, I don’t know if they’re going to get a result there,’ but on the other side there’s teams fighting for their life. It’s been so tight. I think we’ve got equally as good a chance as anyone to stay up.
“We definitely believe we can [avoid relegation], but we realise it’s a tough challenge. We realise that we’ve got to take it each game at a time now and make sure we give everything for that game and try and take maximum points, and that’s all we can do from now until the end of the season and hopefully it will be enough.”
Shorey’s previous club, Aston Villa, also see themselves hovering precariously near the relegation zone following a disappointing first term in charge for Gerard Houllier.
However, Shorey refused to comment on reported problems of unrest at Villa, insisting he did not know the new staff well enough to do so.
“It’s hard, because I was obviously there under the previous manager so I can’t really comment on the way it’s going at the minute, so I really haven’t got an opinion on it because I don’t know the new staff,” he said.
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By Vaishali Bhardwaj
