The stark situation was revealed by Mark Docherty, director of clinical commissioning and service development at West Midlands Ambulance Service.
Mr Docherty was appearing before Shropshire Council's health scrutiny committee to answer concerns over the deterioration in the ambulances response times in the county.
It comes after the Shropshire Star revealed that half of all ambulances sent to Shropshire's two main hospitals are being forced to wait for 30 minutes or more before patients are admitted.
Mr Docherty said: "This weekend we quite frankly ran out of ambulances. There was a period on Saturday where if a cardiac arrest had come in we had nothing to send and that is a really bad thing and we do not want to be there.
"We need help, we need help of the health economy to help us deliver a more effective ambulance service, that is safe."
Mr Docherty said the ambulance service is facing significant problems with delays in transferring patients at hospital.
West Midlands Ambulance Service said there have been 96 delays of more than an hour at hospitals in the past eight days. The target waiting time is 15 minutes.
Mr Docherty said: "The delays are a problem to us because it consumes resources and it ties up ambulances.
"So on Saturday when you had no ambulances because they were delayed at hospital, if you had a cardiac arrest you would not have had the service you deserve.
"The risk I think at times like this is we talk about one hour delays at hospital and target eliminating those, but the target is actually 15 minutes and anything over that is unacceptable."
Mr Docherty told the committee he understood the difficulties faced by Royal Shrewsbury Hospital and Princess Royal Hospital - both are currently having to deal with far more patients than their A&E units were designed for.
However, he described the situation as "demoralising" for ambulance staff who make efforts to get to hospitals as quickly as possible, only to face significant delays when they arrive.
He said: "We have driven over country roads at very fast speeds to take them somewhere appropriate then to stand in a corridor waiting is very demoralising for our staff.
"They have done everything they can to that point
"We are saying we do not want any delays over 30 minutes."