With only three goals from their seven Championship matches, they are the division's lowest scorers but the Portuguese boss tried to look on the bright side after Tuesday night's stalemate at the Liberty Stadium.
"It was a familiar story with chances created but no goals and our best opportunities came late in the game," said Sousa.
"They had a couple of opportunities late on but we had far more of the play all over the field.
"I hope this is a start for us with players coming back from injury and suspension but we need to know the way to play and that is important.
"Our midfield is in transition but they are crucial to the way we play as we try to present quality on the field.
"The spirit was there tonight, which was an improvement on Saturday, but goals are important, although it is necessary first to create and we are doing that so it will bring us confidence."
Swans keeper Dorus de Vries was the busiest in the opening period and skipper Alan Tate was booked early on for a scything tackle.
Evander Sno raced down the flank for the visitors but after cutting inside he fired well wide.
Swansea hit back through Nathan Dyer but he overran the ball when well placed after receiving from Andrea Orlandi.
In the 37th minute, new signing Cedric van der Gun headed against an upright from an Orlandi corner but there was very little goalmouth action as the first half drew to a close.
Neither side made changes for the second half and on the hour, Orlandi headed into the corner of the visitors' goal only for Adriano Basso, the Robins goalkeeper, to scramble away under pressure.
Both sides used all their substitutes in a vain effort to snatch the winning goal and it almost fell to Carl Skuse in the third minute of injury time only for De Vries to block his point-blank shot.
Bristol City boss Gary Johnson said: "I am very proud of my players because they all worked their socks off.
"I am very happy with a point and we could have snatched the victory right at the end.
"It is a squad game now and we have had to make full use of all our players as we have had several going down with a virus.
"Nicky Maynard had to be taken out of the starting line-up after reporting in unwell this morning."