Winger Mackay-Steven and midfielder Armstrong left United for the Glasgow giants in the January transfer window for a combined fee of about £2 million, according to BBC Sport.
Both were important players for Jackie McNamara’s side, and without them the team have struggled.
United are currently fourth in the Scottish Premiership table with 46 points from 27 matches, seven points behind third-placed Inverness Caledonian Thistle but with a game in hand.
The Terrors chairman Thompson has now explained why the club felt that they needed to sell the duo to Premiership rivals Celtic.
"There's no doubt from a footballing point of view it wasn't the right thing to do, but we still believe it was the right thing from a financial point of view,” Thompson told BBC Scotland.
"It's been hard for a lot of people to take that but we've got to run the club as a board. We have legal obligations and we still believe it was the right thing from a financial point of view.”
Is Stephen Thompson’s reason valid?
One can understand Thompson’s reason behind the big decision in January. United needed the money and Celtic were ready to pay it.
True, selling key players in the middle of the season is going to affect any team, but United were never going to win the Premiership title.
The Terrors, who finished fourth in the league last season, are still in with a shout of breaking into the top three.
Moreover, Celtic are arguably Scotland’s biggest club, and it is a step-up in the respective careers of Mackay-Steven and Armstrong.