Captain Luke Parsons said his side has not settled yet but believes they can still win promotion from Bucs Western 4B Division.
They were normally beaten by an impressive Uwe side who plays two divisions higher.
“The squad is still a bit up in the air and we need to establish a starting 11,” Parsons said.
“We drafted some players up from the 3rd team.
“But I am brimming with confidence after today’s match.
“We played a hell of a lot better than we did on Saturday.
“We will definitely be looking for promotion this season.”
Swansea kept Uwe at bay in the first half, but a sluggish start after the restart cost them a goal.
Despite a couple of excellent opportunities they became dominated by Uwe and eventually conceded the second.
“We didn’t capitalise in front of goal when we had the chances,” added Parsons.
“We spread the ball about and passed well.”
Swansea University 0-2 UWE 1sts