The Baggies are currently rooted to the bottom of the standings and four points adrift of safety following last weekend's 3-2 home defeat to fellow strugglers Southampton.
Albion's eight-season stay in the top flight is now under serious threat but former England international Barry insists now is not the time to panic and they must instead take things one game at a time, starting with Monday's trip to Stamford Bridge to take on Chelsea.
"It will be a case of taking things one game at a time,' Barry told the club website. "There are going to be a lot of up and downs between now and the end of the season. It's up to us to make sure there are more ups.'
The 36-year-old conceded the home defeat to Southampton was a bitter pill to swallow for his side but knows picking up results at the Hawthorns is going to be integral to their chances of survival.
"The home form is going to be vital. That's probably why the Southampton result has knocked us a bit," Barry added.
"Before that the results and performances had been really good so it's important to put that one to bed really early, go into Chelsea and then from then on be really positive about our form and take it through to the end of the season."