Roglic overcame a 23-second deficit on the final day's 111.9-km mountain trek from Ondarroa to Arrate, with the 31-year-old leapfrogging overnight leader Brandon McNulty in the process.
Pogacar was tasked with working for teammate McNulty on Sunday (AEST), but the UAE Team Emirates pair were unable to keep pace with Roglic during an attack on the descent with 60 kilometres to go.
In the end, the Slovenian settled for a second-placed finish behind Groupama-FDJ's David Gaudu, clinching overall victory in the process ahead of compatriot Pogacar in third.
During his assessment of stage six, Pogacar conceded the task of reeling in Roglic was virtually "impossible".
“It was impossible to close the gap immediately on the descent," he said.
“If the attack happened on the climb or on the flat, you could follow, but it’s impossible to follow on the descent. It is how it is.
“Of course we would like to have been there when they went but it was just impossible.”
“We had a really wonderful week here,” he added.
“Brandon showed he has good character, he is a really good rider who will be really bright in the future. We had fun this week, we tried and under the circumstances we are happy with this week.”
Pogacar will now turn his attention to La Fleche Wallonne and Liege-Bastogne-Liege, two events set to air LIVE, FREE and in HD on SBS VICELAND and SBS On Demand.
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