Referee Mr Miller turned down penalty appeals at both ends as the Seasiders continued to look for their first victory of the season.
They came closest to scoring on 16 minutes when a clever ball from John Murphy put strike partner Scott Vernon in behind the defence.
The former Oldham man's shot hit keeper Rhys Evans and the Swindon custodian scooped the ball off the line only to see winger Rory Prendergast put in another shot which appeared to have crossed the goal line.
However, despite Blackpool's protests, that was as close as the game got to a winner.
Despite the fact that the visitors from Wiltshire enjoyed more of the possession, especially in the first half, Blackpool's debutante goalkeeper Les Pogliacomi had no saves to make and very little to do as Peter Clarke and Rob Edwards got the better of strikers Rory Fallon and Jamie Cureton.
Blackpool made a more positive start to the second half and could have gone ahead through a powerful shot from midfielder John Doolan but his effort went just over the bar.
Doolan was taken off shortly after the hour mark prompting a sharp exchange of views with his manager Colin Hendry in the dugout.
The best chance of the game did not arise until the 83rd minute when young substitute Simon Wiles hit a deep cross for Murphy but his header at the far post was well saved by Evans.
Blackpool also had a late penalty shout when substitute Simon Grayson went down under a challenge from on-loan Swindon defender Patrick Collins in injury time but again Mr Miller didn't want to know.
At the other end Peter Clarke put in a potentially game-saving challenge to stop substitute Christian Roberts and again a half chance for the goal came to nothing.