Saints won 2-1 at the Hawthorns on Saturday.
Pardew thanked the fans for their unwavering support during what has been a difficult period.
“We started a bit nervously but there was a lot of good energy on the pitch and in the second half I thought we deserved something," said Pardew.
“It's a shame for our fans because I thought they were really good for us today.
“We really appreciate that and we're going to need them over these next 11 games.
“Our goal was a great goal, a fantastic goal. We needed it really, it was a confidence booster for us all.
“That gave us a bit of a grandstand finish, but unfortunately we couldn't squeeze another goal in during that period."