The Spanish coach steered the five-time Cup winners to the quarter finals last season, where they lost at eventual winners Arsenal.
Everton v West Ham United
The FA Cup
Third Round Proper
7.45pm, Tuesday 6 January 2015
Goodison Park, Everton FC
Live BT Sport
Winners receive £67,500 from prize fund
And he is determined his squad is strong enough to have another good run this season, despite an inconsistent first half in their Premier League campaign.
Martinez might change his starting line-up after their New Year's Day loss at Hull marked four consecutive defeats, but he insists he will play a winning side.
"I do not like to say I will experiment, but it is an opportunity to open competition for players and to do it in a different tournament is welcome," he said.
"We are at home against a very good West Ham side. They will come with a good, open approach and I think it will be a fantastic game of football. I want it to be a start of something for us and be a good platform for the second half of the season.
"The FA Cup is best competition in the world in domestic football and we are excited and looking forward to it.
"We have to perform well and we have to win and it's important we have a few days [after the Hull match] to get together and get back to our standards. We have to accept recent criticism and [use it to] make us stronger as a football club."
Meanwhile, West Ham skipper Kevin Nolan believes the good times are returning to the East End of London after Sam Allardyce's side made a strong start to the season.
West Ham last came close to winning The Cup when they lost the 2006 Final on penalties against Liverpool.
Nolan said: "I think a lot of it has to do with the signings he has made during the summer and not only have they been good, but we have not had as many injuries as last year to key individuals. We just didn't have the strength in the squad to cope with it.
West Ham captain Kevin Nolan says competition for places is fierce at West Ham
"This season it has been all guns blazing and when people have gone out with injuries, other players have stepped up and the transformation has been fantastic.
"It was probably what Sam and everyone expected, but not as quickly as it has happened."
The Hammers suffered a nightmare spell in The FA Cup last season when they were thrashed 5-0 by Nottingham Forest in the Third Round and were depleted by injuries going into the game.
But the situation is completely different for Allardyce this time around, with a number of players battling to even get on the bench this season.
The West Ham manager is expected to field his strongest team at Goodison Park and Nolan says the fierce competition for places is making everyone perform to the top of their game.
Nolan added: "There are a lot of great players who are unhappy at the moment because the performances have been so high.
"When you are out of the team you are going to find it difficult to get back in.
"Players like Matt Jarvis, Guy Demel, and Ricardo Vaz Te have not even got onto the bench which shows the strength in depth that we have got."
