She told MPs that some teachers were in danger of ignoring the brightest children, and called for every school to have plans for stretching gifted youngsters.
Ms Morris told the Commons Education Select Committee it was "unacceptable" for bright children to be allowed to coast through school and called for a culture change to give high academic performance "street cred".
"We are very worried about access to some of Britain's top universities, that in many schools if you attend them you do not seem to get access to those universities," she said.
Ms Morris, responding to the committee's report on highly able children, announced a pilot project to run 34 summer schools this year for gifted children. .
Ms Morris said: "Every child should be enabled to reach their full potential in school. Many schools ... neglect the most able."Reuse content