Glen Garrod, the new president of the Association of Directors of Adult Social Services, said the health service was "mythologised" and had become "totemic" in many people's minds, which meant social care was underfunded and found it harder to recruit.
Mr Garrod, executive director of adult care and community wellbeing at Lincolnshire County Council, told the Daily Telegraph that social care "struggles to compete with the beloved NHS that has all this iconography around it. Whilst it deserves that, it can go too far, and we deserve that too".
He added: "We had three days of snow, particularly along the east coast of England, so we were particularly affected in Lincolnshire.
"The media and the public narrative was all about the NHS doing wonderful things. I can assure you there are far more social workers and social care staff out there doing equally wonderful things. Where was our narrative?"
"We don't just fix bits of people, we see the whole person", he added.
He said social care struggled partly because it was organised on a local level, instead of nationally.
"When the NHS was formed it became totemic almost. It was an identifiable construct which had a group of identifiable professions within it. Social care operates through local government in a local environment. Its national profile isn't as powerful.
"There wasn't this national totemic structure where ministers and the public could look and say 'that is the creation of the state, we contribute to it'."
A pay deal cut last month meant NHS staff are set to get a 6.5 per cent pay rise over three years, in exchange for giving up a day's holiday.
Mr Garrod said staff at the lower levels would receive pay increases which were much higher, tempting care workers to leave the social care sector in favour of healthcare.
"If you're a home-care worker, [becoming a] healthcare assistant might seem an attractive option. Particularly if you're going to be able to receive two or three thousand pounds a year more. For home care workers, that's a lot of money," he said.
"Councils are paying more but there's a limit to how far they can go and the NHS is able to go further at the moment. I think that's regrettable. It's not to say that the NHS shouldn't have more, it's to say that we'd want a parity of esteem."
He called for social reformers such as Charles Booth, Sidney and Beatrice Webb and Joseph Rowntree to be celebrated in the public consciousness in the same manner as nursing figures such as Florence Nightingale.
"We've got our own figures - they do not have the same resonance, it strikes me," he said.
Earlier this year the National Audit Office described adult social care as a "Cinderella service" which is undervalued and lacking in prestige, leading to workforce shortages.
A Government green paper due to be published before the summer will set out a plan for social care funding and staffing.