The Spaniard faces a tough task in replacing Moyes, who enjoyed 11 years at the helm at Goodison Park before departing to succeed Sir Alex Ferguson at Manchester United.
|20/1||Everton are 20/1 with bet365 to win the 2013-14 FA Cup
But Jones has claimed that Martinez intends to utilise the foundations laid by the Scot, rather than attempt to immediately impose a new philosophy at the club.
"I think the key here at Everton is to get the balance between what’s gone on before and what we can bring to the table," he told the club's official website.
"What Everton have achieved is sixth place in the Premier League, which is fantastic, and we need to match that and do better over a period of time. It’s a great challenge.
"It’s a fantastic group of players. That’s there for everybody to see. More than talent, you have to look behind that and you can see the character of the players.
"I won’t forget the game at Wigan in October when they were 2-1 down with half an hour to go. The impression from being on the opposite management team was that this group of players aren’t going to stop until they get something out of the game. It was such a positive statement.
"Then you come into the club and you hear about the quality of the people not just the quality of the players. That’s what’s exciting because it is a great platform to start work on."
Jones, who worked alongside Martinez at both Swansea and Wigan, also revealed his delight over being handed the opportunity to join the Merseyside club.
"It wasn’t a difficult decision to join Everton but it was a difficult decision to leave Wigan because I had four years there as a player and four years there as assistant manager," he continued.
"You have a certain attachment to any club - if I have eight years at Everton it would certainly be difficult to leave. You meet good people, but we felt like the time was right, the opportunity is right and we took it. We are ready to go.
"It is the next step for us and it’s a huge club with huge tradition. You notice the great standards straightaway when dealing with the people in and around the club. The club motto certainly rings true."