The Blues squad landed in Bangkok on Friday morning (BST time) to a big support following their 11-hour flight from London Heathrow, and they were warmly greeted as they made their way through Suvarnabhumi Airport.
Martinez's side begin their visit to south east Asia with a game against Leicester City on Sunday, and the Spaniard explained how happy he was to be there.
The club's Twitter feed quotes Martinez as saying: "We are looking forward to getting closer to our Thai fans. It's great to be here. We have been looking forward to playing here. Hopefully the game will be a good advert for the Premier League.
"You are going to see two teams playing attacking football which should make for an exciting match."
Midfielder Leon Osman also talked up his excitement at being back in the region, following the club's visit back in 2005, and the 33-year-old said the whole team are raring to go.
"I came to Thailand nine years ago and the great reception we received then has continued ever since," he said.
"We want to put on a performance. The character is one of the big strengths in the squad. We are a close-knit group."
Meanwhile, new Leicester signing Leonardo Ulloa is part of the Foxes squad that travelled, and the striker is set to play a part against the Merseyside team on Sunday, manager Nigel Pearson confirmed.
"He has joined us in very good shape," said Pearson. "[It is] good business for us. Everton are well established in the Premier League so it will be interesting to see how we perform on Sunday."