Results in February dealt a blow to the Toffees' Champions League hopes, putting even more emphasis on Saturday's FA Cup quarter-final trip to Arsenal.
Roberto Martinez's side went to the Emirates Stadium and earned a creditable league draw earlier this season and Reid thinks that will provide a psychological boost.
"Every league game is important but the FA Cup is special to me and this is a big weekend for Evertonians and Everton Football Club," Reid, who lifted the trophy with the Toffees 30 years ago, told Press Association Sport.
"Everton have done terrifically well but they have to see it through.
"This is the business-end of the season and it would be fantastic to get a result at the Emirates.
"I was at the Emirates in the league game earlier this season when they played well and came away with a point and I think they go back with a lot of optimism.
"I am certainly optimistic about their chances."
Reid acknowledged the advancements made in Martinez's first season, with the team able to compete with most opponents almost on an even footing.
"There is a belief and optimism and certainly Roberto has added that to the side. I think he has done a great job," he added.
"I was at Old Trafford when Everton went there and won earlier this season and I think there is a belief now that they can go to these places and win.
"There has been a lot of consistency about Everton and they are a good team; (Ross) Barkley has come to the fore, (Gareth) Barry has done a great job and James McCarthy has been absolutely fantastic.
"But the most improved player for me is Seamus Coleman, he has been absolutely outstanding."
Key to their chances at the Emirates will be the form of on-loan Chelsea striker Romelu Lukaku, who scored last weekend in his first appearance after a month out with injury.
"I thought Everton were outstanding at Chelsea and Tottenham recently without that cutting edge," Reid said.
"It is important Lukaku is back as Arouna Kone has had a terrible time with injuries and Lacina Traore has had a problem since coming in on loan."