Diego Simeone's side won La Liga for the first time since 1996 at the weekend and could complete a double against Real in Lisbon.
Atleti held their nerve in the title showdown at Barcelona on the final day, with Ramos in no doubt that the newly-crowned Spanish champions have the edge heading into the Champions League final.
However, Juanfran believes Ramos is simply playing mind games.
"I think Sergio was trying to fool people with what he said," said the defender.
"I know him – he's one of the best players in the world. We shared the same dressing room with the national side (and) as far as his comments are concerned, I'm sure he doesn’t really think that.
"They want us to start believing that we are the better team but that's not going to happen.
"There are no favourites. We'll be going into the match with the same humility as we always do."
Atletico will hope for a repeat of their Copa del Rey final success from last season as Simeone's men beat Real at the Bernabeu in extra-time.
While Carlo Ancelotti's team ended Atleti's defence of the competition in the semi-finals in February, Juanfran still believes his side can secure another trophy win against Real.
"Last year it seemed that Real Madrid were the stronger side and around that time, I said that there were no favourites," he added.
"We are the same team as the one which played the Copa del Rey final although we have really grown; let’s hope we can get a similar result this time."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.