Should be graduated before April 1st to apply under Masters quota for H1B?

I am graduating end of April 2014 completing a Masters program. Even though I will have my OPT at that time, I was hoping to look for H1 sponsorship. In this regard I spoke to a few job consultants and they told me that they cannot file H1 under the Masters category since I will be graduating end of April, and one needs to be graduated before April 1st to fall under the Masters quota for H1. Is this true? Will I not be able to apply for H1 on April 1st 2014 under the Masters quota? Please help answer.

Unfortunately, that is true. Still, you can apply in the general quota (which is more competitive).