But as Murray marches into the second week of Wimbledon 13 months on, former British No 1 Tim Henman is adamant the appointment has not only been vindicated but could yet be the key to the Scot lifting a second title at the All England Club on Sunday.
The voices of dissent began as soon as Mauresmo was added to Murray’s camp, with Australian player Marinko Matosevic claiming he could never appoint a female coach because “I don’t think that highly of the women’s game”.
Then, when the Brit was crushed 6-0, 6-1 by an irresistible Roger Federer at the World Tour Finals in November, Greg Rusedski implored him to beg former coach Ivan Lendl to return to the set-up.
Murray, of course, did no such thing and, under Mauresmo’s stewardship, he has returned to number three in the world and today faces Ivo Karlovic for a place in the Wimbledon quarter-finals.
He has more or less cruised through the first week at SW19, downing Mikhail Kukushkin, Robin Haase and Andreas Seppi.
And Henman is backing the Brit to lift the trophy for a second time after his memorable 2013 triumph. “Andy’s got a great chance of going all the way this year and winning his second Wimbledon title,” explained Henman, who is an HSBC ambassador.
“He’s playing as well as I’ve seen him play. He’s had great preparation, so fingers crossed he can keep his form heading into the second week.
“He’s also playing the right way and I think that’s where Amelie Mauresmo deserves some credit because she has made a real difference to him. I just hope it continues.”
Mauresmo, who is with Murray at Wimbledon despite currently being heavily pregnant, has been able to keep the occasionally volatile Scot relaxed during her tenure as coach.
While there is rightly excitement at the possibility of Murray adding a second Wimbledon title – and a third Grand Slam – to his CV, getting past Karlovic today will be no small task, both figuratively and literally, with the Croat standing at 6ft 11in tall.
Karlovic produced a typically powerful display to beat popular Frenchman, and 13th seed, Jo-Wilfried Tsonga 7-6, 4-6, 7-6, 7-6 in round three – making history in the process.
The victory ensured that the 36-year-old became the oldest man to reach the last 16 at Wimbledon since compatriot Niki Pilic in 1976, 39 years ago.
The Karlovic-Murray match will be second on centre court this afternoon, with the winner to face either Viktor Troicki or Vasek Pospisil in the quarter-finals.
Henman is a man who knows a thing or two about centre court, having reached four Wimbledon semi-finals in a five-year span at the turn of the millennium.
And now that Murray has put last season’s injury woes behind him, Henman is convinced that a raucous home crowd can inspire the 28-year-old.
“Having the centre court crowd on your side is the best and I think it could make a difference for him,” added Henman.
“I’ve said many times that if I could have played my whole career on just one court, it would have been centre court at Wimbledon.
“He’s had a good off-season and put the back injury behind him, which I think was key for him heading into the year.”
Henman was speaking after holding a masterclass for last year’s HSBC Road to Wimbledon National 14 & under Challenge finalists on court 19.
The talent on display has Henman convinced that the long-term future of British tennis is in safe hands, while there is also optimism about its short-term future after five Brits – Murray, James Ward, Aljaz Bedene, Liam Broady and Heather Watson – made it into the second round of Wimbledon.
Ward and Watson actually reached third round before heartbreakingly losing to Pospisil and Serena Williams respectively. And Henman is keen to see those results used as a launching pad for home-grown players to join Murray at the top-end of the sport.
“It was nice to have five Brits through to round two of Wimbledon this year – those are good results,” he said.
“We obviously need far greater strength in depth on both the women’s and the men’s side but there have been some good performances.
“We had Murray and James Ward on court on Saturday and, at the start of the day, I felt they could both win those matches.
“Then Heather Watson put in an amazing performance on Friday night against Serena Williams but she’ll be bitterly disappointed she couldn’t find a way to get through.”
• The HSBC Road to Wimbledon National 14 & under Challenge is the UK’s largest national junior grass court tournament and forms part of HSBC’s investment in the stars of the future.