Thompson recently claimed that the BBC's newsrooms had a "massive bias to the left" when he joined the corporation in 1979.
Yesterday, Simpson joined fellow BBC veteran Roger Bolton in criticising the director general's comments about the corporation's news coverage, reports The Daily Telegraph.
Speaking at the Cheltenham Literature Festival, the 66-year-old said: "I was really cross with Mark Thompson for saying the other day that when he joined the BBC 30 years ago it was very left-wing in its political coverage.
"Thirty years ago I was the BBC political editor and there was absolutely nothing either left-wing or right-wing about our coverage. We were as straight as a dye then and I think it is absolutely as straight as a dye now.
"I don't know why Mark said that. Maybe he had some particular people in mind on some of the programmes but in terms of the BBC's core coverage that was not the case and I don't know why he chose to say that."
Simpson also described the sacking of former BBC director general Greg Dyke in early 2004 as an "outrage". Dyke left the BBC in the wake of the Hutton inquiry, which was critical of the corporation's coverage of how Britain went to war in Iraq.
"I think Greg Dyke was by some way the best director general I have ever served under, with the sole exception way back in the '60s of Sir Hugh Green, who was absolutely magnificent and had to fight almost daily battles against Harold Wilson's desire to change things," said Simpson.
"I loved old Greg and I still think he is fantastic. He did wonders for the BBC and for the staff image and he should never, never, never have gone. It was an outrage."
Simpson, who has just signed a new three-year contract with the BBC, expressed his belief that the corporation currently has an "existential problem", a point on which he directly clashes with Thompson.
"We are getting into new ground, new territory, with the BBC. It is an area Mark disagrees strongly with me about. He thinks the BBC's future is much more secure than I believe it to be," he said.
"The reason why I am worried about it and nervous about it is because politicians of both the main parties have discovered a real weakness of the BBC and that is the licence fee. The act of cutting the licence fee is a political act which increases political control over the lifeblood of the BBC."
Simpson warned that the BBC will lose its independence if the government opts to reduce its licence fee funding, as it will become "desperate to keep its lifeline".
He explained: "It's like being water-boarded by the CIA. As your head goes down for the fourth or fifth time you are desperate for the air.
"Who knows, you might do anything then. You might lay off a programme you have made which has irritated the government in power.
"You might go easy. And that's just the beginning of a slippery slope. The present government contains people who are ideologically opposed to the BBC and don't think it ought to exist or be funded in the way it is."