Victory over Real Madrid last season brought Atletico a first domestic trophy since 1996, and Godin has his sights set on further glory.
Diego Simeone's side are level at the top of the league with Barcelona on 49 points from 18 matches, and reached the last 16 of the Champions League after going unbeaten in Group G.
However, Godin has reassured the club's fans that Atletico want to compete in all three competitions this season.
"We are already thinking about Valencia (who they face in the next round of the Copa del Rey on Tuesday)," said the central defender.
"Anybody who thinks that we will be putting the cup to one side this season is mistaken.
Godin's team mate Koke echoed those sentiments ahead of the first leg against Valencia at the Mestalla.
"Valencia is the only thing in our minds and we are only concentrating that, not (the subsequent league game against) Barcelona," Koke added.
"We don’t like to give any side anything and want to win every game we play."
