Clarke included Nicolas Anelka in his starting XI less than a fortnight after reports emerged suggesting the French striker was set to retire from the sport.
The club denied he had ever decided to quit but did grant him compassionate leave following the death of his agent.
Anelka returned to training in midweek and Clarke had no qualms about giving him 90 minutes.
He did not have too much of an impact, though, as goals from Ben Davies and Pablo Hernandez gave Swansea the points and left the Baggies winless and without a goal in three.
"I thought Nicolas' performance was really good and I picked him in the starting XI so I must have been happy with him (in training)," said the Scot, who appeared irked by questions about Anelka.
"Nicolas is part of the squad and he's a good player; his performance showed he is a good player. I think the fans like him, they like the fact that Nicolas Anelka plays for West Brom.
"Of course the crowd are behind him, he's one of their players. He's part of the squad and everyone is happy he's here."
Like Laudrup, Clarke is hoping to add attacking players on deadline day - with his need particularly pressing given his side's record of no goals in three league outings this season.
"I've spoken at length on about the need to bring fresh faces in to the club," he said.
"We have good people who have been working hard to make this club better and make them more competitive.
"I hope there will be some good news for the supporters, we all need good news...even I need some good news.
"I need some players in forward areas that can give us a bit of quality so we create chances."
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- Nicolas Anelka