Roberto Martinez paid tribute to the Hillsborough Family Support Group when he spoke at the memorial service to mark the 25th anniversary of the tragedy on Tuesday.
The Blues boss was at Anfield, where he read a passage from the bible before addressing supporters.
Martinez hailed the families for their persistence in the fight for justice for the 96 victims of the disaster, which occurred during Liverpool's FA Cup semi-final against Nottingham Forest on 15 April 1989.
"It's only recently that I've had the privilege to spend some time in your city," said Martinez. "It's been over 10 months and I've experienced great warmth, great spirit, great friendships, and I've also seen great determination, passion and commitment for ensuring what's right and fair.
"And those are the qualities that represent the Hillsborough Family Support Group - a remarkable group of people. The way you have fought for justice has been truly remarkable.
"For 25 years, you've gained the respect of those within and beyond football, and [also] this city.
"I don't have to tell you Everton are with you. You know that. Everton remembers. We always will."
Martinez recalled learning of the disaster as a teenager growing up in Spain, admitting he had found it difficult to comprehend how fans had failed to return home after what should have been a joyous football occasion.
He added: "I was only 15 in 1989, a football-mad kid from a football-mad family, like many of you [here] today. And we heard the news, we heard about Hillsborough. As a family, we couldn't believe the pain and horror that the families would get from receiving the news that their loved ones wouldn't be coming home - that they wouldn't be coming home from a football match.
"How can anyone die watching the game we love? That isn't right. That isn't fair."
A screening of the Anfield service was shown at Goodison Park, where Everton's first-team squad gathered alongside chairman Bill Kenwright and members of Club staff.
Mr Kenwright later provided his own tribute and followed his words with a spoken recital of the chorus to Liverpool's anthemic 'You'll Never Walk Alone'.
The speech was met by a standing ovation from those inside Goodison Park, before Peter Howarth of The Hollies performed a rendition of the band's hit 'He Ain't Heavy, He's My Brother' with support from the Liverpool Rare choir.
"It is very special for me to be standing here, just as it was to be at Anfield last year," said Mr Kenwright. "It is made more special because we have our first-team squad and academy sitting up there.
"But today is not about Everton Football Club. It’s about Liverpool Football Club and the way they have held their heads high for 25 years.
"The thought of what the families have been through is unimaginable.
"Last season, we had an opportunity to salute the Hillsborough campaigners at a night-time game against Newcastle. We debated what we should do and a [certain] song was mentioned that was very much part of Liverpool Football Club.
"Debate ensued and we didn’t perform that song - we came up with another song that has become very much a part of the Hillsborough campaign (He Ain't Heavy).
"But today I hope that you will share those words, because they are magnificent words. Think today of the 96 and think of those kids, husbands, those daughters who never came home."
