Blackstock has hit 12 goals for Rangers this season and was badly missed as the west Londoners' faint play-off hopes took another dent with a goalless draw at home to Crystal Palace today.
Sousa was informed only by sporting director Gianni Paladini that Blackstock was joining their Championship rivals last week - a decision apparently made by owner Flavio Briatore.
It left Sousa with young Italian Samuel Di Carmine as his only fully-fit striker against Palace - and the Portuguese coach's frustration boiled over when he was sent to the stands just before half-time.
"I gave the players two days off after the Bristol City game and when I came back Mr Paladini told me he had an agreement (for Blackstock) to go on loan," said Sousa.
"It is a decision for the board and only they can answer it. I'm not frustrated, I said from the first day I have to adapt and try to do my best with the players I have."
Sousa, usually one of the coolest customers on the touchline, lost his rag at the treatment being dished out by Palace's giant defender Claude Davis on Di Carmine.
Davis had already caught the striker with a flailing arm which went unpunished by referee Scott Mathieson, but when the Jamaican clattered Di Carmine again by the touchline Sousa came charging out of his technical area.
This time Mathieson booked Davis but Sousa was ushered out of the dug-out and spent the second half in the directors' box, which at least had a couple of spare seats with Briatore and co-owner Bernie Ecclestone on Grand Prix duty.
"I can't understand when a manager is looking out for his player, I care about my players and I went to see him, and I am sent to the stands," added Sousa.
"I said nothing to the referee, I was going to see my player. I think it was because I went out of my area."
Palace boss Neil Warnock, a regular scourge of referees, adopted the unusual role as peacemaker and had sympathy for his opposite number.
"I told him to calm down a bit," smiled Warnock.
"To be fair he didn't do much - he was concerned about his lad who had blood coming out of his nose.
"If he wants me to speak for him I will do - I know everyone on the commission," he added.
Adel Taarabt squandered the best chance of an otherwise pedestrian encounter, Rangers' on-loan Tottenham winger firing over from 14 yards.
Palace's first shot on target came just after the break, when Victor Moses' fierce shot was tipped over by Radek Cerny.
"The pitch was not very good, the first job they should do is get a new one, no matter how many millions you spend on players," added Warnock.
"If we were a bit more clinical we might have finished it off but a draw was probably a fair result."