The SPFL League 1 champions reached the last four last night after winning a replay with Albion Rovers.
United will now meet the Ibrox side at the Glasgow stadium in the first of the semi-finals, with the tie set for April 12. Thompson contacted the Scottish Football Association last week to have the venue changed but was informed that Ibrox would still host the semi-final tie.
The United chairman had been concerned that Ibrox could not be considered as neutral ground for the cup tie. His club confirmed that they intend to ask for an allocation of 20,000 tickets for the match, with the capacity at Ibrox set at 51,082. Thompson is convinced that his club can sell 20,000 tickets given that 27,000 fans attended their Scottish Cup final win at Hampden in 2010.
McNamara last night backed that suggestion and believes that it is only fair his club be granted a fair share of the ticket allocation. He remains opposed, however, to the decision to use Ibrox as the semi-final venue at all. "Like most people, I'm surprised the decision for the semi-final venue was made so early," said the United manager.
"But now it's about waiting to see what allocation we get. Had it been Celtic who got to the semi-final what would they have done? Kept it at Ibrox and split the allocation? There's no doubt we're at a disadvantage. Could they have changed it to Parkhead? Possibly.
"It gives Rangers an advantage because it's their home stadium. It would be the same if the match was at Tannadice because we know the stadium and the pitch. They have an advantage regardless of the ticket allocation but a 50-50 split would certainly give us a better chance [of reaching the final].
"We'll wait and see what the allocation is now that we know who we're playing. I'd like to think we could take half. We've had good backing from the fans. It's a 'neutral' venue so I don't see why we shouldn't get half."
McNamara dismissed the suggestion that he would use their presence at Ibrox to help motivate his players to overcome Rangers and reach the final."We won't use the chosen venue or ticket allocation to motivate the players as if it is some type of injustice," he said.
"The chance to go and play Rangers at Ibrox to get into a final is motivation enough. The venue might give Rangers an advantage but it doesn't change anything for the players or myself to go and win it. If it's Ibrox, Celtic Park or Hampden, the occasion should be the only motivation needed for any player."
The United manager is scheduled to appear before an SFA disciplinary panel before that tie having been charged with misconduct alongside St Johnstone counterpart, Tommy Wright. The two managers became embroiled in an ugly touchline spat at Tannadice last midweek and both were sent to the stand as a result.
It is possible that McNamara will be given a touchline ban - although Danny Lennon and Derek Adams were both given suspended bans following a similar incident last month - but he does not harbour any hard feelings towards Wright as a result of their argument.
"The SFA have been in touch and my hearing will be two days before the semi-final," he said. "You just deal with it. There was frustration on the night but I spoke to Tommy in my office after the game and there were no problems. You get frustrated but Tommy's a nice guy and I get on great with him.
"We played them in friendlies when I was at Partick. We spoke fine after the game but we're both under pressure - everyone is under pressure to get results. I was disappointed to get sent off on the night but more disappointed to lose the game the way we did."
His side would win dramatically on Saturday - United came from behind to beat St Mirren 3-2 - and will push for a European place between now and the end of the season. Their fixture list includes a trip to face League Cup winners Aberdeen at the end of the month, although the Tannadice side will be without Nadir Ciftci and Andrew Robertson for that match. Both players both went past the disciplinary points threshold during Saturday's win as a result of their jubilant celebrations.
"I can understand why Nadir celebrated the way he did," said McNamara. "But he's now suspended and so is Andy Robertson. That's the disappointing thing."