That didn't happen in 2015, and Irsay isn't pleased with the reason why. The owner believes the offensive line has to improve for the team to achieve its ultimate goal.
"We want some leadership," Irsay told the Indianapolis Star on Friday. "When [assistant coach] Howard Mudd was here and it was Jeff Saturday and Tarik Glenn [on the offensive line], the mantra was, 'No one touches 18! His jersey doesn't get a spot of dirt on it!'"
"I mean, it was the pride of the building. I can't tell you the way those offensive linemen carried that pride. We have to get back to that."
Mudd was the team's offensive line coach from 1998 -- Peyton Manning's rookie season -- until 2009.
Luck, who had the worst season of his four-year NFL career, played only seven games in 2015 because of injuries. He went 2-5, and one of his best games -- Nov. 8 against Denver -- happened to be his final game of the season when he suffered a lacerated kidney and a partially torn abdominal muscle. He also missed two games early in the season with a shoulder injury.
"You know I'm demanding with my expectations, and I know the weight of having Andrew Luck," Irsay told the Star. "We want to get to the promised land, and I'm not shy about saying 'more than once.' We'd like to win two world championships when Andrew's with us over these next 12 to 14 years."
Irsay told the Star that the team's "goal" this offseason is to re-sign Luck, whose rookie contract runs out after the 2016 season.
"If we don't get an agreement [this summer], we still have time. And he is going to be signed," Irsay told the Star. "There's a reasonably good chance we can come to that agreement this offseason. He will be here, trust me. Andrew and I have talked -- we talked after the end of the season -- and he couldn't be more excited."
And that fact has Irsay excited about adding at least another Lombardi trophy to the one won by the Colts in Super Bowl XLI.
"If you win one, that's great," Irsay told the Star. "If you win two, it's Hall of Fame and everybody's going. And if you win three, you're starting to get into Never-Never Land."