Eden warned against taking a disproportionate approach to managing trees after a Norwich inquest last week found 11-year-old Daniel Mullinger was killed by a falling branch while on a school trip to the National Trust's Felbrigg Estate.
An investigation by North Norfolk District Council and the Health & Safety Executive found safety management of the woodland was in line with the guidance available at the time.
The inquest's jury returned a verdict of accidental death on 25 June. A council representative said the tree was subject to two-yearly inspections under National Trust policy and had been examined six months before the accident. National Trust representative Nick Champion said: "We were assured in the inquest that our tree procedures and safety management ... were in line with guidance."
Eden said: "This tree has failed with very tragic consequences but we need to make sure we don't make a knee-jerk over-reaction and set standards that are inappropriate compared with the level of risk."
The inquest comes as the 31 July deadline for the consultation on the British Standard 8516, recommendations for tree safety inspection draws closer.
As part of the recommendations, the draft standard suggests frequencies of between a year for basic or layman inspections, and five years for an expert inspection.
It is uncertain whether the standard will be introduced. Eden said the National Tree Safety Group is carrying out its own work into developing an industry standard, part of which included a national conference on safety last month.
Institute of Chartered Foresters executive director Shireen Chambers said the industry needed to agree guidance. "We've got to have a common sense approach; nothing is risk-free, especially with trees, which are a living organism but this must be held in perspective.
"Even if your tree is looked at every day, a branch could come off, but there is an onus on any tree owner to have an inspection regime; people do need some guidance."