What is the age category for your book? If it's adult, then yes, you might have a bit of a problem. On the lower end of 40K is very short, even for a cozy mystery, which usually run in the 50-60K range.
It's also good to keep in mind saying things like you don't have the opportunity to increase the word count is not something an agent wants to hear. Honestly, I'm not even sure what that means. Does that mean you're unwilling to do it? Or that you can't see a way to do it? That you don't have time to do it? Or that you need editorial insight to do it? Because if the latter's the case, get some beta-readers and critique partners and have them read it with the idea "I need to bulk this book up." It will likely improve your chances.
An agent wants to represent an author who is open and eager to revise, because revision is Trade Publishing's thing. If you're lucky enough to get an agent, they'd likely have you revise to bulk the book up before they went on sub, to increase the chances of a sale. And an editor might have you do the same.