"We have peace of mind," Abadia told reporters. "We are not satisfied, of course, but we have peace of mind because we know that we had a very good performance all along.
"We displayed the good football that we have in Colombia, we proved how Colombian football has progressively evolved."
Las Cafeteras - The Coffee Growers - were underdogs in their quarter-final debut, ranked 21 spots below the European champions at 25 and the lowest-ranked team remaining.
But they had already served notice in a 2-1 upset of two-time champions Germany in the group stage that they were not to be taken lightly, and were the last team from the Americas still standing.
Leicy Santos scored in the 44th minute to the delight of the largely pro-Colombian crowd of 75,784 but costly errors by keeper Catalina Perez and Colombia's back line led to goals by England's Lauren Hemp and Alessia Russo.
"We had the determinedness on the pitch but after that second mistake we lacked the finishing," Abadia said.
With dazzling young players such as Linda Caicedo (18), and a fan group unrivalled except by hosts Australia, Colombia captured the imagination of soccer fans in a tournament Abadia called a turning point for women's soccer in his country.
"And these turning points will make us reflect... this is an excellent time but we need to be better than this. I know that we will have the support from the executive committee. Why? Because we've proven what women's football can be in Colombia," Abadia said.
"Today we were a team like Brazil but you know we haven't been there for as many years as Brazil - or the men's football. It's not about being equal, it is about proving what we have in Colombia and how we have to grow from now on."
Abadia marvelled at his squad's supporters, who were in fine form on Saturday - a noisy, pulsating sea of yellow and blue at Sydney's Stadium Australia.
"That has been exceptional," the coach said. "What people did, the people who live here in Australia, every time that we were playing that support was clearly crucial; we were feeling like locals and that was a decisive factor."