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Barker, 22, won the women's 25km points race having previously claimed two silver medals in Hong Kong.
British Cycling have admitted it had not paid "sufficient care and attention" to riders' wellbeing.
"It's about time they had good press about all the good work they do," Barker told BBC Radio Wales Sport.
An investigation into the culture at British Cycling was launched last year after ex-riders complained about their treatment.
In March, British Cycling apologised for any "failings" in its performance programme and promised to be more caring to riders following accusations of sexism and bullying.
But Wales' Barker, who won silver medals in the madison and scratch races at the championships, said she could not have achieved her success in Hong Kong without the support of British Cycling.
"I said I wanted to win the points race about six months ago," said Barker, who won women's team pursuit gold at Rio 2016.
"I went into the British Cycling offices, had a meeting and said 'what do you think I could do to win this?'
"They completely changed my training, changed all my focuses and the coaching and staff were absolutely fine with that.
"I felt so incredibly supported, probably as supported as I did in the lead up to Rio.
"I've been supported throughout my career."
Great Britain won five medals in Hong Kong compared to the nine they won at the previous year's Championships in London.
Barker does not consider the Championships to be a disappointment and said the team was undergoing a transitional stage.
Olympic champions Joanna Rowsell Shand and Sir Bradley Wiggins have retired while fellow Rio 2016 gold medallists Jason Kenny and wife Laura did not compete in Hong Kong.
"The big medal winners weren't there so we didn't expect to have a similar medal haul this year," Barker added.
"We never went in with massive intentions. We took a very young team just to get the experience.
"There were some really positive performances.
"If you just look at the times or the attitudes and the way everybody presented themselves you wouldn't think it was a young team.
"I think they're going to go a long way."
Olympic champion Elinor Barker has praised under fire British Cycling following her victory at the Track Cycling World Championships.