The Swans went ahead through a Wilfried Bony penalty, but the Potters were then awarded a spot kick of their own in controversial circumstances, as Victor Moses went down easily under Angel Rangel's challenge.
"I thought it was a difficult game - Swansea are going to cause people a lot of problems and they did today," Walter told the club's official website.
"To go a goal down against Swansea when they keep the ball so well we knew would be really difficult. We managed to get the goal before half time which was a really good penalty by Charlie [Adam].
"We had a few good chances in the second half and restricted them to long range shots which we were happy with."