Despite going into the Scottish Championship 12 months ago as title favourites, the Glasgow side finished third, 24 points behind winners Hearts.
They later missed out on a place among the elite when Motherwell beat them 6-1 over two legs in the play-offs.
Managed initially by Ally McCoist – a former team-mate of Hateley’s – the team began the campaign brightly enough but unravelled from late November and fell off the pace.
Hateley claimed earlier this week Rangers were ‘too leggy’ in the latter stages of games and pinpointed that as a reason for their collapse.
By contrast, they have already scored four goals in the final 15 minutes of cup matches against Hibernian and Peterhead this term ahead of Friday’s league opener against St Mirren.
Smith, who managed Rangers over two spells between 1991-1997 and 2007-2012, has dismissed Hateley’s comments and offered his backing to McCoist.
The club’s most celebrated goalscorer assisted Smith during his second period at the helm and he is adamant McCoist would never have let fitness levels drop too low.
The 67-year-old said: “I have to say I completely disagree with Mark Hateley’s assessment of that situation. I don’t think for one minute that there has been an issue with fitness at Ibrox.
“I worked for Rangers for years and we equalled the record number of matches played for one season.
“When I left there is no way that Ally McCoist and Kenny McDowall, in any shape or form, would have allowed the fitness to drop.
“The issue last season was not fitness, it was the squad not handling the pressure of playing for Rangers adequately.
Speaking on SPFL sponsors Ladbrokes’ website, Smith added: “I couldn’t say that fitness was the cause of Rangers’ problems last year – that’s not a fair assessment.”