Baxter was angry after the TMO ignored some foul play during the build-up to the second of winger Adam Thompstone's hat-trick of tries on his first start for his new club since moving from London Irish in the summer.
After fly-half Ignacio Mieres had knocked on on his own line, he was taken out off the ball by Leicester number eight Thomas Waldrom ahead of a 46th-minute try which gave Leicester a 23-3 lead.
Baxter admitted the try did not affect the result but he was furious the TMO had missed the incident.
He said: "It's very easy to say it has had an effect on the try. He (Mieres) has knocked on and as he goes to chase the ball he is taken out off the ball.
"What is it if it's not foul play and has not had an effect? To me that's why we have TMOs. Any team in the country would say that if he knocks on, the reason he can't chase the ball is because someone takes him out around the neck."
TMOs have been given more licence this season to look for foul play in the build-up to tries and Baxter said he had spoken to referee Tim Wigglesworth after the game.
He added: "He said the TMO was looking at it and if he sees anything he can tell me."
Baxter said Exeter, who were bidding for their third consecutive win over Leicester, did not deserve to get anything out of a game Leicester dominated.
"That was one issue in a game where in various areas we were not good enough," he said. "I am not running away or making excuses for the result.
"We gave away too many loose penalties, our set-piece wasn't good enough and we did not take our chances.
"There's a lot of things for me to look at other than a TMO decision."
Thompstone is the eighth player to score a hat-trick for Leicester on his first start and only the second since 1935. Fijian Marika Vunibaka was the last to do it in 1997.
The 25-year-old, a replacement against Harlequins last week, only found out he was playing on Friday after Scott Hamilton withdrew due to injury.
He scored once in the first half and twice in the second, with England fly-half Toby Flood kicking 15 points. Replacement Ben White scored a last-minute try for Exeter, with Mieres kicking a penalty.
Leicester director of rugby Richard Cockerill praised Thompstone and his squad after a difficult week due the withdrawal of several players, some at the last minute, taking the number in the treatment room to 12.
He said: "Adam is a quality player. He has had some horrific bad luck with injuries in the last three of four years and has been playing second team and getting his fitness because he missed a bit of pre-season with a bang on the head.
"We have had a lot of injury issues, guys dropping out on the day with illness and slight ailments, but I thought the attitude of the squad against a good side was fantastic.
"It was a very good performance and we defended exceptionally well so I was disappointed with their try.
"Before the game I'd have taken just a win. After the game you look at the opportunities we created and you'd be disappointed not to get a bonus point, which shows how good a performance it was against a good team.
"Our attitude to putting our bodies on the line was what we wanted and needed after last week, and I thought Toby Flood's reaction after taking some criticism last week was really good. He kicked well and ran the game well."
Cockerill said he expects some of his injured players to return to training next week, including England pair Ben Youngs and Manu Tuilagi.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Lions get ready for their matches with this green training jersey. It's what the players wear. Get in the Gear!
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.