"It's a new Everton but still the same philosophy," said Mauricio. "They have a great manager and great players. We have a lot of respect for Everton."
Mauricio finally had the full squad together after the international break on Friday including new signings Serge Aurier, Davinson Sanchez, Fernando Llorente, Juan Foyth and Paulo Gazzaniga.
"Now it feels like the real competition has started," he said, with a nod to the start of the Champions League and a Carabao Cup third round tie this month - indeed, seven matches before the end of September.
"We start to build a new dynamic and get to know each other to be a strong team with a strong mentality.
"We need to manage everything in the right way to try to get the best from the players."
Everton signed a number of players in the summer, most notably Wayne Rooney returning to his boyhood club from Manchester United, ex-Spur Gylfi Sigurdsson, Michael Keane from Burnley and goalkeeper Jordan Pickford from Sunderland.
Another arrival is striker Sandro Ramirez from Malaga. "He’s a great player," said Mauricio. "He was at Barcelona and Malaga and he’s a very good striker. We need to vigilant about him.
"As I said, they are a little different from last season but they keep the same mentality, the same manager and it will be tough."
Mauricio knows his opposite number Ronald Koeman well.
One of the great players of his era, Koeman helped Barcelona win four La Liga titles in a row under Johan Cruyff and the Dutch international famously clinched Barca's first European Cup with the winner against Sampdoria at Wembley in 1992.
Mauricio moved to Barcelona's city rivals Espanyol from Newell's Old Boys in 1994. "It was difficult to beat him, he was at Barcelona, I was at Espanyol," explained Mauricio. "We played a lot of derbies. I think I beat him once. He was a great player, a fantastic player and part of the ‘dream team’ under Johan Cruyff, a fantastic team in football history."