A 2-1 success at The Hawthorns moved the home team into seventh place and put them three points clear of their visitors with nine games remaining in the season.
Hopes of qualifying for the Europa League are therefore realistic and, although he does not want to speculate, Clarke wanted a platform to build on from a victory over Swansea.
"For the confidence of our players and the enthusiasm of the group to attack the last nine games, it was important we got three points at home," he told Sky Sports.
"It is nine victories at home this year. There are not too many other teams in the league who have won nine games at home.
"Hopefully the supporters enjoyed the game and the occasion and they go home happy tonight."
Former West Brom player Luke Moore had given Swansea the lead before Romelu Lukaku equalised prior to half-time and the striker then had a penalty saved by Michel Vorm.
West Brom took the lead through a Jonathan de Guzman own goal but Swansea could have equalised before the final whistle only for Roland Lamah's effort to be wrongly disallowed for offside.
Clarke said: "We got a break at the end, because the Swansea goal that would have made it 2-2 was not offside. It came off Ben Foster last.
"But sometimes when you put as much effort and quality into the game, you get a little break."