No, I do not agree with this statement.
There are many other determinants of demand beside price, like:
1. Income: Income determines the purchasing power. Rise in income will lead to a rise in demand of a commodity and fall in income will lead to a fall in demand of a commodity.
2. Price of Substitute Goods : Demand for cheaper substitute goods will rise when there is fall in price of such goods. E.g. when sugar price rises, then the demand for jaggery will rise.
3. Price : Demand for a commodity is mainly influenced by its price. Normally at a higher price the demand is less and at a lower price it is more. Thus, demand varies inversely with price of a commodity.
4. Nature of Product: Under necessary and unavailable circumstances the demand of a commodity will continue to be same irrespective of the corresponding price. E.g. medicine to control blood-pressure.
5. Size of Population: Demand for commodity depends upon size and composition of population like age structure, gender ratio which influence demand for certain goods. E.g. larger the child population, more will be the demand for toys, chocolates, etc.