Davenport, herself a former world number one, who won three grand slam titles including Wimbledon in 1999, said Konta proved in her three-set Centre Court victory on Wednesday against Donna Vekic that she had the steel needed to get to the top.
"I think yesterday's match was a great example of that. I always look at players and look at their weaknesses and if those are improved upon.
"To see her on Wednesday just being a mental rock out there under some really difficult circumstances was in a way inspiring," Davenport said, adding that in the past Konta had buckled under pressure.
"We have seen other players just crumble under the pressure of their own country and she stood up, she never panicked, she never blinked, she never had that look I've seen before of looking over with almost scared eyes, that was gone.
"You get a sense that is something she has worked incredibly hard on, the discipline to be focussed on each point in the routine she has talked about and it proved itself in one of her biggest moments here," she said.
Davenport said that she had noticed Konta's relentless focus when watching her practise.
"Watch the discipline she brings, watch the intensity she brings," she said. "It is hard to see success won't come for her, it is impossible to know."
Davenport said it would be interesting to see Konta at every level in all the majors to judge whether she was able to maintain the aura of Wednesday "because it was awfully impressive".
The American said she sensed in Konta the same level of dedication that her compatriot and defending men's champion Andy Murray showed.
"I get the sense with her, like you do with Andy Murray, that everything she can do to get better, she is doing. That could be mentally, physically, recovery, on the court.
"It is hard not to see success for someone who is willing to put in that amount of effort and that much time and discipline to their career at that age."
(Reporting by Simon Evans; editing by Clare Lovell)
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