The Cottagers secured a point thanks to Ivan Cavaliero's second-half header.
And Parker believes the result was fully deserved.
"I thought we were outstanding tonight from start to finish, performance wise, with the ball, everything," Parker said.
"No one really knows what we have been through the last couple of weeks, players out there tonight who have had one day of training, I am proud because of how we played in the circumstances but I am even more proud of them because we showed real quality tonight.
"The second half, the way the game was going I felt the second goal was coming. You have someone on the pitch there like Ademola Lookman who carves chances out of nothing.
"All round I thought our general play tonight was superb. I am very, very pleased.
"In this division for us every game is going to be massive. We showed our quality today and had our identity about us and that is what pleased me the most.
"There is one thing you do need and that is first and foremost is spirit but you also need quality. You need quality to stay in this division and we showed that in abundance tonight."