Marsh was only given out after big screen replays showed him jamming a Matt Henry delivery onto his toe, before it ballooned back to the bowler, prompted a late appeal from New Zealand.
Hastings said he felt the original appeal before the replay was "very stifled" and Australia captain Steve Smith said after the match he felt the episode had been handled "pretty poorly".
The incident followed New Zealand captain Brendon McCullum's criticism of Steve Smith's decision to stick with an appeal to dismiss England batsman Ben Stokes for obstructing the field in a one-dayer at Lords in September.
Stokes argued he was merely protecting himself when Mitchell Starc threw a ball back at the stumps in attempting a run out, and McCullum suggested Smith "may live to regret" the decision.
Smith later admitted he was disappointed by the comments.
Tensions have been running high between the Australian and New Zealand teams since last year's World Cup final at the MCG.
Australia wicketkeeper Brad Haddin was criticised for giving New Zealand batsmen Martin Guptill and Grant Elliott exuberant send offs after being dismissed in the match.
-news.com.au