Most of the replies already given address a lot of things to consider. My few cents for consideration:
(1) Avoid Speculation
Bad things can and do happen. Interview both the exiting group and the current staff. Get a better understanding of anything that might be broke, then start a plan to fix it. Keep your existing staff "in the loop".
(2) Look Again for Hidden Talent
Some of your existing staff may have promotion potential, if not management potnential. Delegate new tasks and watch how they respond. Give them an opportunity to manage a new process, lead a group, become responsible for something greater.
(3) Define the Gap
What gaps exist with the exiting people? Do you really need 3 replacements to do the job? Were they effective/efficient to begin with? What exactly did they support, and do you need more or less people to do it?
(4) Identify Solutions to Fill the Gap
First, fill the gap. Do you work your existing staff overtime until the other positions are filled? Do you bring in temp/contractors in the meantime? etc., etc... It'll be easy to cause your existing staff to burnout if you don't offer some relief. Filling 3 spots can take awhile. This may also be an opportunity for one of your staff to supervise a contractor, giving you more feedback on their capabilities. Identify your "ideal/preferred" and "next best" approach to managing the gap.
(5) Secure Resources
Go back to your management, if necessary, to get the resources you need for an approach identified in #4, above. You may be surprised to get waht you ask for. You may also get shut down and forced to work with what you've got. In either event, you need to show that you've got the situation in hand and are not afraid to say you've got difficult times facing you.
(6) Take the Time to Find the "Right" People
As some other responses have indicated, don't fill to get a body in, fill it with someone that'll be a good "fit". Perhaps a headhunter placement agency could be of assistance (if so, identify it too in #4), maybe you'll have to search a little longer, whatever. Give yourself the time (again, resources in #4) and pad it a little to find the right people.