The Spain international was reported to have been the subject of an approach from Barca after playing a key role in Atleti's Liga title triumph, which was sealed with a 1-1 draw at Camp Nou on the final day of the season.
But Koke signed a new contract with Atleti in June, putting pen to paper on a deal to keep him in the Spanish capital until 2019.
And the 22-year-old has now revealed that he did not feel it was the correct time to leave, with Atletico also having reached last term's UEFA Champions League final - where they were beaten by arch-rivals Real Madrid - as well as lifting their first Liga crown since 1996.
"The truth is that part of me said it was difficult to say no to Barca but I wanted to continue at home, at the best time for many years at Atletico," he told AS.
"It wasn't time to leave. This is my home, where I feel wanted and the club didn't need to sell. How was I going to leave at the best time for Atletico?
"It's not easy to say no to Barca and that interest is appreciated. It means the work I've done has paid off. But I'm at home."
Diego Simeone's Atletico squad has undergone something of a transformation during the transfer window.
The likes of Diego Costa, Filipe Luis and Adrian Lopez have all left the club, while winger Antoine Griezmann and striker Mario Mandzukic have come in.
But Koke does not think his choice to stay makes him a huge player for Atleti.
"I'm just another player at Atletico, a player who gives everything for his team and does what the coach asks," he added.
"I'm not the best or the flagship, the banner. The most important thing to me is to make a better Atletico and be a team player, which is ultimately what matters.
"[The new signings] are great players, they're all important and I believe they will all contribute a lot to the team.
"They hope to do things right and that is something the coach values highly."
