Rovers took the lead in Saturday's Premier League clash at the Stadium of Light, had two goals disallowed and saw new signing Nikola Kalinic pass up four glorious opportunities as the Black Cats came from behind to snatch all three points.
To add to Allardyce's misery, skipper Ryan Nelsen limped off with a recurrence of his medial ligament injury and striker Franco di Santo damaged a hamstring.
Allardyce said: "I have left a group of players in the dressing room who are very disappointed.
"We are all very disappointed that we haven't come away with anything today based on the performance.
"But this is the Premier League, this is the cruellest league in the world for punishing somebody that doesn't take advantage when they are in control."
Rovers went ahead with 21 minutes gone when Gael Givet smashed a long-range shot home after Lee Cattermole had cleared Morten Gamst Pedersen's corner to the edge of the box.
The had already had a Jason Roberts goal cancelled out for a foul on keeper Marton Fulop by Christopher Samba, and Allardyce was aggrieved at referee Alan Wiley's decision, even if he could accept Steve Nzonzi's second-half effort being ruled out for offside.
He said: "It was a bizarre decision, to say the least, from Alan Wiley.
"I have reviewed it from several angles on the replays - if that's an infringement, then there would be 20 free-kicks and penalties given in every game every week."
The Black Cats were level within 11 minutes of Givet's opener when Kenwyne Jones out-stripped the Blackburn defence to collect Steed Malbranque's ball over the top and round keeper Paul Robinson.
He headed home Cattermole's cross nine minutes after the break to put the home side ahead, but Nzonzi's header was ruled out for offside against Samba seconds later.
Samba also hit the bar and Kalinic failed to make the most of a series of openings as Rovers' luck deserted them.
Sunderland boss Steve Bruce admitted his side had ridden their luck.
He said: "We just simply couldn't cope with Blackburn in the first half, so we were itching to get them in at half-time and to be level was good for us.
"In the second half, we were much, much better and dealt with the physical capabilities of Blackburn a lot better because in the first half, we simply couldn't cope with it.
"I did talk about fixture congestion - it's ridiculous in this part of the season. They [Blackburn] are fresh as a daisy and you could see that.
"We rode our luck a little bit today, we have to say."
Meanwhile, Allardyce revealed he had left Stephen Warnock, who has been heavily linked with an £8million switch to Aston Villa in recent weeks, behind after they decided he was not in the right frame of mind to play.
He said: "He is at home because he struggled to focus on this game and didn't feel that mentally he was capable enough of giving his best, so we both took the decision to leave him back at Ewood.
"There have been no developments on the transfer front, but he didn't feel and I didn't feel that it was the right thing to do to play him."
Asked if Warnock could leave before the transfer window closes, Allardyce said: "We will wait and see what next week brings, but we haven't had anything near a bid we could consider to be enough, so he is still our player and I envisage that he still will be our player.
"If anything, from my point of view, we need him to be our player even more because of Ryan Nelsen's injury today."
Bruce also confirmed that his interest in Bordeaux striker Marouane Chamakh, also on West Ham's shopping list, is ongoing.
He said: "It's a possibility. We are still interested, of course, but we will see what develops."