Blaming Wade is a bit unfair. Like yeah, taking the two was stupid, but he still did better than most, and he made runs in the first innings as well. Faced the most balls on this pitch of any player (though Pujara might catch him second dig) and scored the most runs other than Smith. I do think he should have upped the scoring rate earlier and protected Haze better but you obviously have to blame the people who actually got out first.
I don't rate him much and I think Nevill is better but this might honestly be his best ever test as a batsman so not the best time to make the case.
Anyway, the reason for losing the series is largely the lack of a second truly successful batsman. After Smith there's a gap of nearly 300 runs to Renshaw, and then Handscomb/Wade/Warner/Marsh all in a group with averages in the 20s (high teens for Marsh), one or two important knocks but no big scores and no consistency. I don't really think any of those guys had a totally horrible series, Warner's getting a lot of criticism but he still made a couple of contributions, as did everyone else, but nobody actually did well overall. You throw in a Renshaw hundred converted from a 50, Handscomb turning a start into a half-century some time before Ranchi, Marsh making a score at some time other than when runs were at their hardest to get, Warner "coming off" one time and smashing the new ball bowlers out of the attack etc and you have a potential series changing result. You just can't win in India with only one successful batsman carrying you, even in a lower scoring series like this one. Australia never actually achieved the goal of batting 150 overs they set pre-tour, only won a test on the most difficult batting wicket, and only really posted competitive scores on the back of Smith hundreds.
Spinners were relatively even, seamers were competitive and kept the runs down even if Umesh had the better series, India had two strong, consistent performers with the bat and some role players and Australia only had one. That's the difference between the sides.