Woodward hit out at Australia captain Harry Wilson's decision to boot the ball out when the Wallabies trailed the Lions by eight points in the final play of the first Test match in Brisbane.
Lock Nick Frost had just won a lineout against the head and with the Wallabies claiming possession inside their own 22 and no hope of winning the match from there, Wilson decided enough was enough.
Woodward, who coached the Lions on an unsuccessful tour to New Zealand, losing the series 3-0, slammed the back-rower's decision, believing that it was an indication of Australian Rugby's 'losing mentality'.
"It was not what a Lions series should all be about. What summed up the game for me was that with the clock in the red and with the Lions winning 27-19, the Australian captain, Harry Wilson, kicked the ball out to end the game," he wrote in his SportsMail column.
"Talk about a losing mentality. For me, it is the last play of the game, so why not have a mentality to try and score, as this could be the situation in seven days' time, only closer?
"Why not rehearse this scenario? Why would any player, especially the captain, want to end the game? That in so many ways reflects the current state of Australian rugby, which is clearly not in a great position."
His remarks have been met by strong backlash Down Under with Wallabies legends Michael Hooper and Matt Burke both hitting out at the former England boss.
England-born Potter has followed suit when he was asked about the remarks ahead of the second Test.
"I think it's pretty ridiculous to suggest that the 23 players who played on the field that played at the weekend have a mentality of losing," he told reporters.
"We went out there to win the game, and we didn't win the game but it was our intention very much.
"You could tell after the game that every one of the 23 players wanted to win that game."
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