With the transfer window closing on Monday, Clarke has expressed his frustration and nervousness at his lack of strength in depth.
Albion have brought in five players without spending a penny - Diego Lugano and Nicolas Anelka on free transfers, with Goran Popov, Matej Vydra and Scott Sinclair arriving on loan.
Clarke is adamant he requires at least two more forward players, but any deals are in the hands of chairman Jeremy Peace and technical director Richard Garlick.
"Richard and the chairman are trying as hard as they can to make some deals fall into place," said Clarke.
"If we could get business done before Monday then it would be much better for my state of mind and for my health.
"But it's difficult. When you look around and ask 'Where can we spend our money?', the market is condensed. There are not so many targets.
"It's going to be hard for us at this late stage to pull a rabbit out of the hat. It's going to be a tough few days for us.
"I'm concerned that we've left it too late and maybe we don't get the right players in to help the squad I've got. It's a good squad, but they do need some help.
"At the moment I can't say I'm confident of landing any player. Time is short, I'm getting a little nervous, but hopefully something will come.
"Rather than for me as a present, it would be a nice gift to the squad I have here."
There is further frustration for Clarke given his role which means as head coach, rather than a manager, he simply makes recommendations, but then has to sit back as Peace and Garlick take control.
"My job as head coach is different. I'm not a manager, I don't have a budget, I can't decide who I'm going to go after," explained Clarke.
"The contract of a head coach is such the club has the final say on who comes in and out of the club. It's the same in my case.
"I can make recommendations, but it's down to the club to bring those players in. My job is to train the players I have.
"Is it frustrating not to have your squad together before the season starts? Yes.
"Is it frustrating to be sitting here now not having made a big-name signing, or a big-cash buy during the summer? Yes.
"But my job is to get over that and make sure the players we do have here go out and give their best for the club. That's what I have to do."
Asked why the club had left it so late, Clarke replied: "That's not a question for me is it?
"That's a question for Richard because that's his job - sporting and technical director.
"You can't really ask me about club policy. You have to ask someone from the club on that."
One iron in the fire is Chelsea midfielder Victor Moses, with Clarke believing he is available on loan.
For Sunday's game with Swansea, Clarke at least has Anelka back after being away for a week on compassionate leave, with his return timely given Vydra is out for a short period with a hamstring problem.
With goalkeeper Ben Foster out for 12 weeks with a stress fracture of a bone in his right foot, Boaz Myhill should start despite a wrist injury.