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."
As the countdown continues for RWC2015, Tournament Chief Executive Debbie Jevans visited the Millennium Stadium to discuss preparations for the eight matches and reveal the positive news that 100,000 tickets for games at the home of Welsh rugby have sold in the last seven days.
Jason Harries is targeting a first win on the World Series circuit this season with Wales. The series returns to action this weekend in Dubai where Harries is part of a team hoping to build from its efforts in round one in October.
Wales skipper Jevon Groves says his side have addressed a few points from Gold Coast and aim to 'hit the ground running' in the next two rounds of the World Series, kicking off with this weekend in Dubai before heading off to South Africa next week.
Wales Sevens manager Steff Thomas is hopeful his side can build from a quarter-final spot in the opening round of the World Series in Australia when his side take part in the forthcoming double header in Dubai and South Africa.