An Antoine Griezmann hat-trick inspired the Spanish champions to an impressive second-half comeback at San Mames on Sunday, after Mikel Rico had put the hosts into a half-time lead.
Atletico head into the mid-season break in third place, just four points adrift of leaders and arch-rivals Real - although Carlo Ancelotti's men have a game in hand.
Full-back Juanfran knows that mounting a sustained challenge to La Liga's traditional superpowers Real and Barcelona - who sit three points above Atletico in second - is easier said than done, but feels his side can do just that in the new year.
"I've always said it is not easy to compete with Real Madrid and Barcelona," he said.
"We must stay the same, behaving as a team and always give joy to Atletico and [make the fans] proud.
"I think they feel that way because they see their Atletico Madrid always competing among the best."
Juanfran also revealed that some wise half-time words from head coach Diego Simeone inspired Sunday's second-half turnaround in Bilbao.
"In the first half they were strong and managed to play against us in a way that we were not comfortable," the Spain defender added.
"At half-time the coach made us change both the mind set and the way we played."
