Dr John Sentamu made the comment in an article for schoolsweek.co.uk.
In it he said children are increasingly missing out on Christian mentoring and care, as well as creative or extra-curricular activities, because schools are packing in more lessons in order to get kids achieving certain grades.
He also revealed that the Church of England has been asking headteachers at their schools what challenges they're currently facing.
The Church runs 4500 primary schools and 200 secondary schools and is also the biggest sponsor of academies in the UK, with involvement in nearly 500.
Around 15 million people alive today had a Church of England education.
The archbishop said: "Shrinking budgets and teacher recruitment featured, but many were concerned that they felt under pressure to sacrifice the most imaginative opportunities that school could offer, in favour of meeting inflexible measures.
"That could mean subjects such as music and PE being squeezed out in primary schools or pastoral time restricted to make way for extra tuition.
"Too many children are missing out on the chance to learn through wider and extra-curricular experiences which provide the kind of learning opportunities needed to foster positive mental well-being and personal growth."
Speaking on Premier's News Hour Clive Ireson, from the Association of Christian Teachers, said: "One of the problems is with school budgets at the moment what people are beginning to cut back on are the teaching assistants. It's often the teaching assistants who do a lot of the pastoral care and support them at times of need.
"A lot of these things, if they were picked up in the primary schools and support [was] given in the primary schools to these children, then we could prevent problems later on.
"Obviously if the child isn't happy, they're not going to achieve the results needed either, because they're not going to be able to concentrate on their work... We have to have the right staff in place to enable that to happen."
A Department for Education spokeswoman said: "Every young person should have access to an excellent, well-rounded education.
"We know subjects like music, arts and PE can transform lives and introduce young people to a huge range of opportunities, which is why we are investing millions in supporting these activities."
Listen to Premier's Alex Williams speaking to Clive Ireson on the News Hour:
