Jenrick approved plans for up to 189 homes at the unallocated 12-hectare site near Nantwich last month, even though the council could demonstrate a five-year housing land supply.
A Cheshire East Council spokesperson said the authority would raise the matter with Jenrick himself.
The decision letter said the secretary of state, who followed the recommendation of a planning inspector, "has taken into account that nationally it is a government policy imperative to boost the supply of housing, and he considers that this benefit should be afforded significant weight".
The letter also said the scheme's provision of 30 per cent affordable homes "is a tangible benefit and merits significant weight".
However, the council spokesperson said the ruling itself "recognises that the application is not in line with the development plan overall and is not in accordance with policies within the Cheshire East Local Plan Strategy, the Crewe and Nantwich replacement local plan and Stapeley and Batherton neighbourhood plan".
The demonstrated five-year housing land supply "should mean that the government's policy of 'tilted balance' in favour of housing development no longer applies within Cheshire East", the spokesperson added.
Despite this, Jenrick "has assigned more significant weight to the government's drive to build more houses [nationally] in making his decision" - which would "be to the detriment of the residents of Nantwich".
But the spokesperson conceded: "Having sought legal advice, it is with deep disappointment that we have been advised that the secretary of state has acted lawfully and there is no basis on which to launch a legal challenge. We cannot support the use of public money to make a legal challenge where there are no identified legal grounds on which to do so.
"Nonetheless, the council will be raising this matter directly with the secretary of state and would encourage our partners who share our concern to do the same."
Councillor Toni Fox, cabinet member for planning, said the secretary of state's decision "has effectively blocked any opportunity for the council to lodge a legal appeal", adding it "clearly goes against the principle of local decision making and will add even more pressure to local services that are already under strain due to the number of new houses being built".
Fox added that she would pursue the matter "politically through our joint administration in addition to lobbying for the support of the borough’s Conservative MPs".
The Ministry for Housing, Communities and Local Government has been approached for comment.