The EFI partition is used to store firmware updates, so they can be installed the next time you start up your Mac.
First, to try to recover it, try to repair the partition map. Hold Command and R keys while your Mac is starting up to start up into OS X Recovery, and open Disk Utility. Then, choose your hard drive at the top of the sidebar (the option with the model identifier of the hard drive, not with Macintosh HD) and repair it. The EFI partition should be created again, so try to install the EFI update again.
If it doesn't work, you will have to format the whole hard drive and reinstall Mac OS X
In disk utility from the command+r boot repartition the drive as one partition on the Partition tab.
You should not of used Disk Utility to delete the Windows partition. You should of used the Boot Camp Assistant app to remove it. If you had read the boot camp instructions it would of informed you of that.