Barnes tumbled under Angel Rangel's challenge, and Sousa said: "From my line of view I thought the referee would give a yellow card to their player for diving but instead he gave them a penalty.
"We started the game well and put them under pressure but they changed their style in the second half and closed down our space as well as adding power up front. But it still looked like 0-0 until the referee gave that decision.
"Normally we dominate games but if you don't have the luck, particularly with refereeing decisions, then it becomes difficult."
Perhaps unsurprisingly, Baggies boss Roberto Di Matteo had a different opinion on the incident and said: "It was a clear penalty as Giles Barnes had put the ball beyond the defender before being brought down."
Second-placed Albion lined up with a five-man midfield in an attempt to stifle Swansea's free-flowing passing game, resulting in very little goalmouth action with neither goalkeeper being forced to make any saves.
Swansea's Nathan Dyer did strike the post with a shot from the byline but Albion rarely threatened the home goal.
It had all the makings of a scoreless draw until substitute Barnes won that penalty. Dorrans' spot-kick went in off the post and it was a different game in the last 10 minutes.
The Baggies slowed the game down and, as Swansea went looking for an equaliser, Dorrans sent a long ball out of defence for Miller to chase and round Swansea goalkeeper Dorus de Vries before slotting home into an empty net.
Di Matteo added: "It was important that we got something from this game.
"Swansea don't concede many goals but they don't score many and I knew that at some stage through the game we would have a goalscoring opportunity.
"We have now put ourselves in a very good position after working very hard all season and must continue to work hard so that we can stay there."
Source: Team Talk
Source: Team Talk