Long important for Baggies - Clarke
According to West Brom, the move collapsed when Hull were unable to stand by their original offer for the player, leaving Long in limbo and still at The Hawthorns.
Both Clarke and the club have been keen to make it clear that Long was not surplus to requirements and that the proposed deal simply made good business sense - and that the 26-year-old still has a big future at West Brom.
"Shane Long is a very, very important member of our squad," said the Baggies head coach.
"I've always said that. I said it all through last season and ever since I came in. He's here, and I'm delighted he's here.
"I spoke to him on deadline day but I haven't spoken to him since because he's been with his country and out of respect for them he has to concentrate and do what he has to do for Ireland.
"He'll come back from there and we will sit down to have a chat and work out how we go forward from here.
"Shane has got a big contribution to make this season."
The general consensus is that Long is savvy enough to remain professional rather than taking the saga personally.
"Only time will tell," said Clarke. "We'll sit down and talk about the situation. He's here, he's part of the side and he has a big part to play."
Sessegnon and Anichebe were joined by Marseille midfielder Morgan Amalfitano and goalkeeper Lee Camp in signing for Albion on transfer deadline day and Clarke admits last week's international break bought them some time to bed in.
"This year the break came at a good time," said the Scot, whose side have just one point from their first three Barclays Premier League games.
"Last year we were a bit disappointed it came when it did because we had started well. This year we haven't started well.
"It's nice to have got a little breather and done some good work in training, with a number of boys away on international duty.
"It was a busy transfer deadline day when we brought in some new players to help the group and I've managed to have some of them around in training to start working towards what will hopefully be a successful season.
"Since deadline day when we had Lee Camp, Morgan Amalfitano and Victor Anichebe come in and they've been able to train with the group, which is good. Stephane has been away with his country.
"We're definitely in a better place as a squad because the squad is stronger now. It's competitive. Now we just need to get them working together and picking up points."