Campbell Fisher, 56, admitted at the High Court in Glasgow, causing the death of Robert Cunningham by careless driving on Prestwick Road, Ayr, on November 19, 2010.
He was originally charged with causing death by dangerous driving, but the Crown accepted his guilty plea to the reduced charge.
Advocate depute Iain McSporran, prosecuting, said: "The accused has been employed as an ambulance technician then paramedic with the Scottish Ambulance Service since the early 1990s.
"Part of the training involves safe driving of ambulances on emergency calls. This requires drivers to treat red lights as give way signs, so the ambulance should be brought to a halt and may proceed through the red light at a speed not exceeding 10mph once the driver has satisfied himself it is safe to do so."
The court heard that Fisher was driving an ambulance service rapid response car.
At 4.48pm the ambulance service received a 999 call from a man complaining of chest pains in Allison Street, Ayr.
The call was allocated to Fisher, who was six miles away at Prestwick Airport. However, just moments after the fatal crash the call was downgraded from top priority to a non-emergency call on the vehicle's on-board computer screen. Mr McSporran said: "It would be accurate to describe the call as an inappropriate use of the 999 emergency system.
"The information which would have instructed Mr Fisher to stand down appears to have been communicated to his computer screen moments after the fatal collision. Mr Fisher had no way of knowing he was not in fact attending a life-threatening emergency.
Mr McSporran continued: "The accused was driving his ambulance car too fast for the prevailing road conditions and either failed to notice the red traffic signal which he was approaching and Mr Cunningham making his way across the pedestrian crossing and struck him, or, having seen him, failed to take action.
"While the bulk of the evidence points strongly to Mr Cunningham having been using the crossing properly - there is evidence suggesting that he was either oblivious to the flashing blue lights and siren of the ambulance or had elected to cross notwithstanding the situation."
Police investigators estimated the speed of Fisher's vehicle before braking as being 46mph and stated in a report: "The blame for this collision must lie entirely with the accused."
The court heard that a car coming in the opposite direction had stopped for the light.
Seconds after he hit Mr Cunningham, Fisher attempted resuscitation, without success.
He was in a state of apparent shock and told the police: "He just walked out in front of me, I didn't see him."
Mr Cunningham, who suffered numerous fractures to limbs and the spinal column that were not survivable, had mild cerebral palsy and basic learning difficulties. He was diagnosed as having schizophrenia that was controlled by medication, and lived in supported accommodation.
His support worker described him as "independent and happy". He is survived by two sisters and two brothers.
Mr McSporran added: "Medical opinion is that a combination of his medication and some alcohol he had that day may have resulted in a decreased appreciation of speed and proximity of traffic."
Judge Lady Stacey banned Fisher, of Dalmellington, Ayrshire, from driving in the interim and deferred sentence on him until next month.