But Thompson hopes that Saturday's Irn Bru Cup final win over St Mirren can be the catalyst for a Premiership return.
When asked if missing out would mean failure, he said: "That's probably a bit unfair on Raymond. It's his first year at the club.
"He had a huge task on his hands and we've got eight games left."
United, relegated at the end of last season, have slipped 14 points behind Scottish Championship leaders Hibernian after a run of four league defeats and a draw.
They lie in fourth place but could yet win promotion via the play-offs in what is McKinnon's first season in charge after joining from Championship rivals Raith Rovers last summer.
"The task was probably bigger than he thought it was, but we are where we are and we'll see where we go in the weeks ahead," Thompson told BBC Scotland in his first media interview in 10 months.
"I know it's the Challenge Cup, it's not a League Cup final or Scottish Cup final, but it's still a trophy and there were over 3,000 fans there at the weekend and they were delighted.
"A lot of fans were happy at the weekend just to get a bit of fun back again, a bit of success, and hopefully it's the turning point for Raymond and the players to push on for the remaining eight games of the season."
Thompson was speaking after a club annual meeting on Monday that he admits "was slightly difficult".
"It was what I expected, but the results in the last year weren't the best and it's the costs of relegation at the end of the day," he said.
"The losses we made last year were quite substantial and there are lots of reasons behind that.
"The top line was down £1.2m in income, we had redundancies and we also spent a lot of money trying to stay in the league.
"So people are perhaps not happy with that, but you've got to remember the previous year was also one of the most profitable in the history of the company."
Thompson, who inherited control of the club from his late father, has faced calls from fans to leave the club but stresses that no potential buyer is on the horizon.
"I made it clear at the agm that there has been no formal approach for the club - to buy the club or speak to the club," he said.
"If anyone has a properly funded proposal, the board and the majority shareholders are here to listen - come and speak to us about the ownership of the club.
"There's nobody come forward in the last year.
"Nobody has come in here and said 'we'll give you a pound and we've got £2m to run the club for X number of years'.
"There have been groups formed, I get that, they are entitled to do that, but is the best way not to engage?"
McKinnon has admitted that United's chances of winning the title probably ended on the day they lifted the Challenge Cup as Hibs extended their lead with a 2-1 win over second-top Falkirk.
However, United can narrow the gap on third-placed Greenock Morton should they beat Ayr United at Tannadice on Tuesday evening.
"We never give up, but you can see it's going to be very, very, very difficult," McKinnon said of their title chances.
"But we just need to concentrate on what we do and keep working on performance levels and, wherever we finish up, we have to take it from there.
"You would rather be going into the game on the back of a cup final win than a defeat.
"You can certainly see a spring in their step in training and it might just be the perfect tonic for us for the rest of the season."
It would be unfair to brand manager Ray McKinnon a failure should he fail to win Dundee United promotion, chairman Stephen Thompson has said.