Engine management light?

Hi, two days ago my focus started to make a whining noise and the engine management light came on. The following day the car could not be started. Turns out that the alternator had failed so I booked the car in and had this replaced. After picking the car up I noticed that the engine management light was still on. I called the garage asking them to clear the light as I thought it was caused by the alternator failure. The garage said that the alternator failure would not have made the light come on and said I would have to pay for a diagnostics. Is this true.