Desmond O'Sullivan, 52, of Linacre Lane, Bootle, Merseyside, admitted causing unnecessary suffering to the black and tan collie-cross in October.
He was given a six-month community rehabilitation order and banned from keeping animals for five years by South Sefton magistrates on Monday.
Unemployed O'Sullivan was also ordered to pay the £180 vets bill and £70 costs.
'In shock'
The court had heard O'Sullivan had been detained by a member of the public after dropping the dog from a bridge in Seaforth on 18 February 2002.
The dog, which was "hobbling and in shock", was picked up by a passing motorist and taken to a vet but died later that day of internal injuries.
Defence solicitor Daniel Dennis said the dog had been a family pet for five years and had been obtained from a rescue centre and O'Sullivan had "cared well" for it in the past.
He added: "A sober person would not have picked up a dog of that weight on a bridge, a drunk person would."
After the hearing, RSPCA inspector Helen Smith, said: "This was a despicable act and obviously I am happy with the disqualification order which I think in the circumstances was fair."