By FOX Sports staff
Although Real have long been regarded as one of Spain's two biggest clubs along with Barcelona, the Rojiblancos have improved greatly in recent years and have won the Copa del Rey, two Europa League titles and two UEFA Super Cups since the 2009/10 season.
And Godin believes the amount of silverware they have won is something that have put them ahead of Los Blancos, who have only won one La Liga crown, the Copa del Rey and the Spanish Supercopa in the same time.
"Now Madrid [are] in our shadow for we have won five titles in recent years," he said. "This is very hard to accomplish.
"We went out twice as champions of the Europa League, a tournament that might not be at the level of the [UEFA] Champions League, but it gives prestige to the club and to the players.
"The fans are thankful for Atletico's titles, which ultimately is the most important thing."
Godin did however admit that his team continue to face an uphill task to challenge the likes of Real and Barca when it comes to the La Liga title, especially given the fact that they operate on a more modest budget.
"It is difficult to compete against clubs with a high budget," he added. "But we are a team and we are characterised as so, and as a team we become strong and competitive.
"With our weapons we fight against other clubs, but in the Spanish league it is difficult to do so for 38 games, as well as play in the Copa del Rey and the Champions League. Sometimes the competition is exhausting.
"The first goal we have is to play the Super Cup against Barcelona, the best team in the world. But we want to win.
"Then we hope to be in second or third position of the Spanish league, which means earning a place in the Champions League. This gives prestige and economic resources to the club."
Atletico will be playing in the Champions League this season after finishing third in La Liga last term.