Souness' team were forced to come back from a goal down after just five minutes, but Andy Cole's 52nd minute equaliser helped ease Rovers' relegation fears.
The incident in question came shortly after Kevin Phillips' opener, Brett Emerton latching on to Tugay's through pass to advance on goal before falling under challenge from Graeme Le Saux.
Blackburn have not had a penalty all season and Dean's decision to ignore the event infuriated the Rovers manager.
"We don't get the decisions, we don't get a fair crack of the whip," bemoaned Souness.
"We're not one of the big teams and we'll have to accept we won't get a penalty this year."
Managerless Southampton will be disappointed to have let a gift of a lead slip especially with the goal with which Cole ultimately equalised.
Their caretaker boss Steve Wigley said: "Our point was deserved especially on first-half performance. We were comfortable, but in the second half they came back into the game.
"It was a poor goal to concede, we had opportunities to clear it."
Similar questions could be raised about Blackburn's defending for the opener, their inability to shut out the opposition has proved a major headache for Souness this season.
And the old problems re-emerged with the game just five minutes old, a simple high ball from midfield was nodded down by James Beattie and Phillips had all the time in the world to pick his spot beyond Brad Friedel.
The Southampton front two were looking particularly dangerous in the early stages, but Blackburn it was who should have dragged themselves back into the game soon after.
First, Emerton was sent through in the incident that so annoyed Souness before debutant Martin Andresen's pass picked out Jon Douglas in plenty of space ten yards out. Unfortunately, for the home team out came Antti Niemi to block superbly.
Rory Delap went close with a header at the other end, Friedel forced to tip over the crossbar at full stretch before Phillips flashed a decent effort just beyond the far post.
After an unacceptable first-half showing, Blackburn made two changes at the break, Dwight Yorke and Matt Jansen coming on for Paul Gallagher and Douglas.
And the substitutions had immediate effect, Rovers looking much more lively than in the first half.
Indeed, many behind the goal thought Andresen had scored a spectacular equaliser on 47 minutes, but his dipping volley dropped just over the top.
It did not matter as Blackburn did deservedly level matters with a scrappy goal five minutes later.
Yorke and Jansen caused confusion in the Southampton box before the ball span kindly off Jason Dodd to Cole, who thumped a low shot past Niemi.
Cole's movement was causing major problems, on 55 minutes he latched on to a Jansen pass, terrorised Claus Lundekvam before drawing a great save from the Finnish keeper.
Shortly after, Blackburn's impressive left-back Michael Gray made a trademark dart down the left before cutting inside and trying to feed Cole with an intelligent through pass. Niemi spread himself bravely and claimed.
Wigley hauled off flamboyant French winger Fabrice Fernandes on 62 minutes, sending on Neil McCann in his place before Blackburn defender Markus Babbel was booked for unceremoniously dumping Phillips to the floor.
The resulting free-kick went all the way through to Delap at the back post, but he could only shoot an unbalanced effort into the side-netting.
Similarly, another free-kick from the left, this time swung in by Dodd only needed a touch to restore the lead, but eventually Lucas Neill was able to smuggle it behind for a corner.
Delap strode forward twice in two minutes to cause Rovers' defence problems, first firing a low drive from 25 yards that Friedel was down smartly to turn away, before charging down the left and feeding Paul Telfer to scandalously blast a superb chance into the crowd.
In between time, Cole raced on to a Yorke through pass only to see Niemi out to make another top-drawer save. Anyway, Cole had been flagged offside in the build-up so it would not have counted.
The Finn's excellence ensured he deserved his slice of luck with eight minutes remaining as Emerton's deflected cross looped up off the goalkeeper, but out of harm's way.
Ultimately, Souness had to be content with a point after his side's dreadful start and was understandably pleased with their recovery after the break.
"We gifted them a goal, Phillips was left with so much room in the penalty box," he explained afterwards.
"It was disappointing, but in the second half we showed our stuff and after the goal I thought we would have gone on and won."
Man of the Match: Andy Cole - Rescued Rovers with an excellent finish and generally caused the Saints defence problems all afternoon.