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."
Meet the members of the WRU's inaugural Youth Board - after an online selection process which saw a host of high calibre candidates submit video applications the WRU has made its first 15 appointments.The board is made up of individuals aged between 16 and 21, and will meet for the first time at Principality Stadium on Monday 15th February.
The Wales Women's team headed to Dare Valley Country Park on a team bonding exercise as the entire squad got together for the very first time in preparation for this season's Six Nations championship which kicks off on Saturday with a clash against defending champions Ireland, in Donnybrook.
Wales Head Coach Warren Gatland discusses his team selection for the opening round of the RBS 6 Nations where he leads his side against Ireland, on Sunday. As WRU TV's Luke Brodley discovers, Gatland is fully aware of the challenges the defending champions pose