"Obviously we were really disappointed with our performance last week. We know we are better than that," McMillan said. "Unfortunately, this team generally performs at its best when our backs are against the wall.
"I am just stoked overall that the boys put in a performance they can be proud of. It wasn't perfect. There were still a lot of missed opportunities and I think we gifted them a couple of soft tries but we will take the win and look forward to Waikato."
Otago led 7-0 early before two former Otago players made huge plays for the Steamers.
Openside flanker Hugh Blake crossed for a try after smart build-up work from fullback Chase Tiatia. Blake then latched on to a Mike Delany chip kick to storm ahead and set up another attacking raid that led to a penalty by Delany for an 8-7 lead.
From the kick-off blindside flanker Tom Franklin, against the team he played 50 games for, set up great ball for the Bay and Terrence Foketi cashed in with a sharp run to the try line.
Otago were ahead 13-12 at the halftime break but despite dominating territory could not break down the staunch Bay defence.
Then came a turning point in the match. From a turnover 70 metres out, Delany kicked intelligently and winger Joe Webber scored after a great chase by Monty Ioane.
Bay led 24-21 with 13 minutes left to play before Tiatia scored a fine try. Crucially Delany missed his fourth conversion but the Bay were up 29-21 into the final 10 minutes.
Otago struck back with a converted try to cut the lead to one point, before replacement halfback Luke Campbell scored the late matchwinner by the posts.
Coach McMillan is looking for Bay of Plenty supporters to fill the Tauranga Domain against Waikato on Saturday afternoon.
"There will be plenty of motivation. They are in that relegation zone so we know they will come and give everything, and that is what we expect of our boys.
"It will be a real humdinger and hopefully we will get an enormous crowd along to bring the boys home. If we win we are sitting in a semifinal and potentially a home semifinal if results go our way.
"Certainly lots to look forward to."
Bay of Plenty 36 (Hugh Blake, Terrence Foketi, Joe Webber, Chase Tiatia, Luke Campbell tries; Mike Delany con, 3 pen) Otago 28 (Fletcher Smith, Jona Nareki, Matt Faddes tries; Smith con, pen; Josh Ioane con, 2 pen) Halftime: 15-13 Otago