The Sky Blues' sole major honour remains that 3-2 FA Cup triumph over Tottenham at Wembley, a day Pressley jokingly admits he is reminded of at every opportunity by former City goalkeeper and current coach Steve Ogrizovic.
And he wants his squad of 2013/14 to leave their own mark on the world's oldest domestic cup competition - starting with Friday night's first-round trip to AFC Wimbledon, formed following the demise of Wimbledon FC, who memorably won the competition just one year later in 1988.
"The FA Cup is a big competition, I've said this a number of times," manager Pressley stated on Thursday afternoon at the club's Ryton training base.
"I don't want to hear about Steve Ogrizovic talking about '87 all the time, I want these young players and senior players to make a name for themselves in this competition.
"In the last 26 years since winning it, the club have reached the quarter-finals on two occasions but 19 times they've only progressed one round or less.
"The fans of this football club have been starved of relative success, there's no doubt about it but they've remained hugely loyal. And I desperately want our players to repay them for that, I really do.
"I think the supporters have been crying out for heroes for a long time since '87 and it would be nice if this group of players could give them hope again."
Coventry will be aiming to build upon the impressive form they have shown so far this season when they meet their lower league opponents at Kingsmeadow.
Having started the campaign with a 10-point deduction, the Sky Blues are now up to 11th in Sky Bet League One - just three points off the play-off places - and are currently enjoying a six-match unbeaten run.
Friday night's first-round clash certainly has an air of romance about it following the two clubs' respective achievements of the late 80s.
And Pressley, who won the Scottish Cup three times as a player, is certainly excited by his first taste of FA Cup action as a manager south of the border.
"I like to look at the history of a football club and look at their achievements because, ultimately, that's what football clubs are built on - their history," he said.
"But we have to start making our own history as a team. We don't always want to be recognised as the team of '87 at this football club. And I think the players are also determined to do that.
"It would be terrific if we could put some form of cup run together, certainly starting with the game on Friday night.
"Make no mistake, we're under no illusions just how difficult a game it will be. AFC Wimbledon are on the back of a very good result against top of the table Rochdale last weekend and they will have confidence from that.
"Also, because it's a cup tie, under the floodlights, live on TV, they will have an intensity about them so we need to make sure we're ready."