The Swans grabbed a 1-0 win at The Hawthorns as Craig Beattie came back to haunt the club he left in August with the only goal of the game in the 50th minute.
Sousa was in no doubt about the importance of the result after only taking charge of Swansea in the summer.
"To win away against the top team in the table is an important night for me," he said. "It was an important three points for us, it gives us a lot more confidence.
"When you win an important game like this one, an away game, against the team that's top of the table, a team that is going for promotion, it is always important.
Confidence"It tells us we are in a good way and this is what we wanted. When you get victories, you get more conviction and more confidence."
West Brom head coach Roberto Di Matteo felt under the weather and so did not attend the post-match press conference.
But assistant Eddie Newton admitted the Baggies had spoken about Beattie before the match.
"We know what Craig can do, we told the boys what he possesses - the negatives and the positives," he said.
"And we got hit on the sucker punch, a little bit of naivety and we got punished for it."