Both new signings were withdrawn during the pre-season loss to Nottingham Forest, but manager Alan Irvine does not expect lengthy spells on the sidelines for either
The centre-back was making his first public appearance for the Baggies following his move from Manchester City after recovering from a calf problem, but last just 35 minutes after coming on a half-time.
Pocognoli, recruited from Hannover last month, was withdrawn four minutes from time after going down under a strong challenge at the City Ground.
Irvine revealed that Lescott had sustained a knee problem, while the Belgium defender had been struggling with a minor hip and groin niggle, but expects both to be fit for the start of the season.
"I've just spoken to Joleon and he feels okay," Irvine said. "He just felt something on the outside of his knee. He felt it when he was warming up and when he cleared from the corner of the pitch he felt it go.
"He says it has settled down now. He was a little bit worried about it at the time but it has settled so hopefully it's nothing too bad.
"As far as Seb is concerned, he had been complaining in the first half about being a bit tight in his groin and hips.
"We did a bit of work on him at half-time and then, of course, he got clattered going for a header. At that point, I just thought 'take him off'."