just like 老布 said, it's business

you shouldn't get business mixed with personal feelings. It may not be natural to you but you have to learn that's the way to deal with these issues. You're in a consulting firm after all, handling such interaction should be 2nd nature.

Do it in person with your manager in a straightforward way. Don't hide behind email or voice mail. Don't behave like you did something wrong. Quite the contrary, you did something right, you realized better value, which your current employer failed to recognize. If someone has to act like the guilty party, it's your manager. NOT YOU.