Barker fumbled the ball into her own net on 75 minutes to deny her side a battling point after they had weathered enormous pressure from the Swedes.
But Pauw was also proud for the fight shown by her side against a team whose players ply their trade in professional leagues around the world.
“That one little mistake cost us,” she told reporters. “The more experienced teams will punish you when you make a little mistake.
“We should be going forward more, making more in our attacks and creating more chances, but these are the players we have got at the moment so I can’t ask for more than they are giving,”
It was another narrow loss for the side after 1-0 defeats to Netherlands and world champions USA in recent times as well.
“We have had narrow defeats to the likes of the United States and the Netherlands and this result again shows that we’re getting closer,” Pauw said.
“I told the players at half-time that they were playing too many long balls into the space in the Swedish half. There was a lot of space there and I asked for us to get forward quicker so that we could capitalise on that.
“This has been an incredible journey for us and the improvement we are showing is giving us a really good chance to start getting results against these higher-ranked sides.
“There is a tremendous energy in the squad and what we are really lacking is goal-scoring opportunities. But when you have a look at where we’ve come from to where we are now, I’m sure you can see the tremendous growth in our football. We showed it again today. We are getting closer.”
Banyana’s next game is against China on Saturday.