MPs have called for more investment in preventative services, warning that cuts represent a "false economy" in light of spiralling costs at hospitals across England.
The council's budget for addiction services was cut by 9% between 2017-18 and 2018-19, falling from £9 million to £ 8.2 million.
Alcohol-related admissions to hospital meanwhile increased by 27% in Nottinghamshire between 2008-09 and 2017-18, from 4,370 to 5,531.
The figures were obtained by a Freedom of Information request by the Labour MP Liam Byrne, who is chair of the All Party Parliamentary Group for Children of Alcoholics.
Mr Byrne said his own father died in 2015 after a long struggle with alcohol addiction.
He said: “Every child of an alcoholic comes to learn the brutal hard way that we can’t change things for our parents – but we can change things for our children.
"But frankly that’s harder if addiction treatment budgets are being cut left, right and centre.
"It's simply a false economy. We’re spending money dealing with A&E admissions when we should be trying to tackle the addiction that lands people in hospital in the first place.”
The FOI figures show there were 335,000 alcohol-related hospital admissions in England last year - 39,000 more than during 2009.
Meanwhile, more than 70 councils cut their addiction services budget last year, while 50 are planning cuts for 2019-20.
Around one third of local authorities say they do not have a strategy in place to support the children of alcoholics - Nottinghamshire among them.
A Department of Health and Social Care spokesperson said: “All children deserve a stable and happy place to call home, and it’s heartbreaking that hundreds of thousands of children growing up with alcohol-addicted parents in this country are robbed of this.
“In December, we committed to funding the National Association for the Children of Alcoholics’ helpline expansion, so that more children in this difficult position have rapid access to support and advice.
“Robust government action has led to a fall in alcohol consumption in recent years – but we remain committed to tackling alcohol-related harms and protecting the innocent victims of addiction.”
Nottinghamshire County Council public health consultant Amanda Fletcher said: "When the responsibility for commissioning of substance misuse (drug and alcohol) services moved over to Public Health and the Local Authority in 2012/13, the historical variety of commissioned services had never been formally tendered so value for money was simply not known.
"After an open tender CGL won the contract to provide Substance misuse treatment and recovery services in Nottinghamshire from October 2014. Since then, over the life of the contract, CGL has been an exceptional provider and as reviewed all aspects of the system and made numerous efficiencies.
"Due to reductions in the public health grant allocated to local government, Nottinghamshire County Council as commissioner and CGL as provider have had to work together and the reduction in contract value has been completed without negatively impacting on frontline staff (i.e. no redundancies), service delivery/accessibility (i.e. there are no waiting times) or achievement of contractual outcomes (all are over-performing). Therefore, it could be considered that the current provision now represents exceptional value for money.
"Currently, the county council is out to open tender for a new all-age substance misuse treatment and recovery service that tackles inter-generational substance misuse through a family-based approach, anticipating that this service will be in place from April 2020. Utilising this “think family” approach, interventions will be put in place to support the children of parents who are misusing substances.
"Additionally, in 2018/19 the Nottinghamshire Integrated Care System (ICS) has prioritised alcohol as a “prevention priority”, acknowledging the serious local burden that alcohol places on the health and care system and an alcohol harm reduction action plan is now in place, led and delivered via a multi-agency working group."