Wales lock Cockbain was forced to leave the field after being up-ended by Woodcock mid-way through the second half.
The incident was reminiscent of the controversial spear-tackle committed by All Blacks Tana Umaga and Keven Mealamu against Brian O'Driscoll in the first British Lions Test.
But the Welsh management confirmed they would not press for further action after studying footage of the incident.
Coach Mike Ruddock said: "We have looked at the video and spoken to Brent and we will not be citing any New Zealand player. If the independent citing officer decides to do so then that is not up to us."
The Welsh Rugby Union has awarded a unique 'President's Cap' to a specific group of players who represented their country between 1945 and 1979, but missed out on international recognition at the time.
Prabhat Mathema, the WRU's National Medical Manager explains the four part Pitchside Suspected Concussion Assessment process the IRB has devised that is being implemented throughout the Dove Men Series and in the LV= Cup this season, which includes the provision for a five minute temporary substitution to allow an assessment to take place.