Diego Simeone led the club to a 10th La Liga title last season - and first since 1996 - as Godin's header earned Atletico the draw they needed in their final league match of 2013-14 against Barcelona at Camp Nou.
Simeone has forged a winning mentality at the Vicente Calderon, but has seen key players move on to pastures new in recent months, with Thibaut Courtois returning to parent club Chelsea, where he has been joined by talismanic striker Diego Costa.
David Villa also departed, but Atletico have made a fine start to 2014-15, with their 2-1 win over Real Madrid at the Santiago Bernabeu on Saturday coming just a couple of weeks after their Supercopa de Espana triumph over their fierce city rivals.
With the likes of Mario Mandzukic and Antoine Griezmann recruited to fill the void left by Costa and Villa, Godin believes the current squad is showing the same characteristics as seen last term.
"I wouldn't say that the squad is better or worse," he said.
"We have different players; we need to play a different way. The team does maintain the same mentality and that's certainly the key."
Godin also paid tribute to defensive partner Miranda, as the pair continue to forge a strong relationship at the heart of the Atletico backline.
"Each of us knows our role in the team at the back," he said. "Having said that, if we can manage to score a goal or two, even better."