Saints moved out of the bottom three as Oriol Romeu's 23rd minute effort was added to by Ward-Prowse shortly before half-time.
"It's a big relief. We know we need to beat the teams around us to pick up important points. You could feel the positivity, which I think stemmed from us in the changing room," said the midfielder.
“You could feel the determination to put things right after a difficult two games and we wanted to put what happened here last time at Cardiff to bed.
“It was important [to start well] but I think it was more important the way we managed the game in the second-half. We spoke about it after the Cardiff game when we got back into it that maybe we should have settled for a point in the situation we're in.
“To manage the game and look comfortable like we did shows we've learned and developed under the manager with the training we've been doing."