Slovenia international Oblak signed a fresh four-year deal near the end of last season, tying him to the LaLiga club until 2023.
Atleti had declared their intention to upgrade the goalkeeper's release clause almost 12 months earlier and Diego Simeone confirmed talks were underway as early as November.
The impasse fuelled transfer rumours and the 26-year-old conceded there were times when he considered whether other clubs would value him more.
"Yes, there were doubts," Oblak told Marca. "It was strange. But that's the life of a professional footballer.
"I was calm that everything would be fine and get resolved. It took a very, very long time, but you sit down, you look into each other's eyes and say what you think and feel, and you reach an agreement. That's how we arrived [at a new deal].
"I know the club, the players and coaches all respect me.
"With the new contract, this story being in the press every week is over. That also gives me peace of mind on the matter."
The new agreement increased Oblak's buyout figure from €100million to €120m, a paltry number in comparison to the staggering €800m release clause inserted into former team-mate Antoine Griezmann's contact at Barcelona.
"Clauses are just numbers in contracts," the ex-Benfica gloveman said.
"If the intention of the player is to continue and the club for you stay... the number changes nothing, no matter if it's €1m or €200m.
"The most important thing is that both parties are happy and follow the same path."