Martinez says he was taken aback when he learned of O'Neill's departure - but reckons things like this go with the territory of being in the Premier League.
"Obviously we don't know what the internal situation is at the football club," Martinez told the Wigan Evening Post.
"I have to say it has come as a surprise to everyone that Martin left before the end of the season. But changes are normal these days - you just learn to get on with it.
"The new man will bring in a completely different approach, and probably that is part of the reason why this league is the best in the world.
"It's colourful, it's exciting, it's unpredictable. That's why people love it so much.
"I'm sure the media will be happy, but Sunderland are a phenomenal club with a great tradition and they're capable of finishing the season strongly."