The Toffees face Chelsea in the quarter-final on Saturday, 21 years after they last won the trophy.
It was Rideout's close-range header on the half-hour mark that proved to be the winner when the Merseyside club beat Manchester United at Wembley 21 years ago to complete a miserable season for Sir Alex Ferguson's men, as they also missed out on the league crown to Blackburn Rovers.
But ahead of Everton's quarter-final with Chelsea on Saturday, the man who seemingly has a great affinity with the competition - having famously scored a hat-trick to help unfancied Tranmere come from 3-0 down at half-time to beat top flight side Southampton in 2001 - claimed that the team that Martinez has assembled is stronger than the one that won the trophy more than two decades ago, and could go all the way this time around.
"That day at Wembley seems like it belongs to another world. I look at the current Everton side and, with respect to my old team-mates, they are much better than the team who won the Cup in 1995," he told the Mirror.
"The talent, especially down the spine - John Stones, Ross Barkley, Romelu Lukaku - is frightening. Results have been inconsistent, and they have thrown away a lot of points in the last five minutes against Bournemouth, Stoke, Chelsea and last week to West Ham.
"But in recent years, Everton have always given as good as they got against Chelsea, and I'm beginning to think it could be their year again."
As Rideout alluded to, Everton's biggest problem this season appears to be their lack of consistency. There is no doubt that when they are on form, they play some of the most exciting football in the Premier League. However, their open style appears to have landed them in trouble on a few occasions this term.
And while the club's supporters may have become disappointed that their league season looks set to finish in unspectacular fashion - as while they are some way off the bottom three, they are also unlikely to finish in the European places - that may enhance their chances of ending their long wait for silverware as it may allow Martinez to concentrate on emulating the achievement Rideout and his teammates managed.