Ranieri's side enjoyed a respectable ninth-placed finish in his first full season, having finished 10th the season prior.
It was during the Italian's second season during 1998/98 when he left his mark at the Mestalla.
A goal from Mendieta and Claudio Lopez double sealed a dream 3-0 win over Atleti on front of 45,000 at Estadio La Cartuja in Seville.
The key to Ranieri's success at Valencia was forging a disciplined and focused defence that revelled on the counter-attack in his familiar 4-4-2 formation.
And Mendieta has explained to Tribalfootball how Ranieri's style wasn't immediately embraced by his players.
"Working with Ranieri in the beginning was difficult because it was a different mentality and a different way of training," Mendieta said.
"But as soon as we understood each other, manager and players and players and manager, everything bonded and everything brought results.
"We felt comfortable with the system and with the way he understood football. The results were there and we had some great seasons under him."
The counterattacking style would of course lead to Ranieri's greatest ever achievement as a manager - winning the Premier League with Leicester City in 2016.
To call Leicester heavy underdogs would be the grossest of understatements. The Foxes were paying 5000/1 to claim the title before the season begun.
And Mendieta says he understands exactly how Ranieri was able to achieve success.
"I could relate that to Leicester because Ranieri's teams are always very competitive," added the former Spain international.
"You could tell this not only with Leicester winning the Premier League trophy, which is unbelievable... but also Leicester being competitive amongst other big clubs in the Premier League.