Sundowns are the only South African side left in CAF competition this season, with the club set to meet DR Congo outfit AS Vita in the second round next month.
Kaizer Chiefs were knocked out in the first round by Ivorian giants ASEC Mimosas on the weekend, while Bidvest Wits and Ajax Cape Town were also eliminated early into the second-tier Confederation Cup.
"The media is supportive guys," Mosimane says.
"For me I don't have a problem because the whole week we read was Champions league, back pages and all that.
"It's been good support for Champions League with you guys doing your part and we are trying.
"We don't want the mentality that South Africa teams are softies, they don't take the Champions League seriously and they always complain.
"But we need proper support hey."