It would take a better half-court offensive design combined with players possessing stronger fundamental skills.
The ability to create better scoring opportunities more consistently against the toughest teams would allow our defense to be even more potent. If we scored more, other teams would be forced to produce more points. That's tough to do when we have a Final Four defense like we did in 2013 and in the tournament this season (though our press was really as important this year in the Sweet 16 and Elite 8 as the zone). Unfortunately, our half-court offenses were inconsistent at best both seasons, and our lack of execution hurt us against teams with really good talent.
Our heavy reliance on random ball screens as our main offensive weapon produces poor spacing, little ball movement, and little off-ball player movement. This makes defending us easy, especially for the solid-to-outstanding defensive teams that are likely to populate the Final Four most seasons. When teams take away our ball-screen offense, we essentially counter with the pin-down screen plays and the Double Fist (double high ball screen) plays. Those plays are fine, but if a defense takes away the initial option(s) on them, we are right back to the random ball screens. The defense wins.
An offense with better spacing, more actions (back screens, flare screens, backdoor cuts, zipper cuts), and an actual inside presence (post-ups) that can be adapted for year-to-year personnel changes would help. For example, Villanova runs a 4-out 1-in motion that stresses ball screens and dribble penetration, but also includes backdoor cuts, screening away for teammates, post-ups with "rip" action (two basket cuts in succession with the other two players filling behind the cuts), and high-low action. The offense builds all of this into the design, and players are taught to "take their lane" based on what the defense takes away. Watching Nova's players execute it makes me salivate at the thought of what G, Malachi, Trevor, and Lydon could do in it.
Do we have to run Villanova's offense? No. But we need an offense that works in some way like theirs: one that uses a series of actions that allows our players to take advantage of defenses no matter how they play. Bill Self's High-Low Offense is another example of such an offense, though dribble penetration can be limited in it. My favorite multifaceted offense (other than Nova's) is one that would be tough to run in college because it takes a full year for players to really get comfortable running it: Gregg Popovich's Motion. It is my favorite because, as an option-based motion, defenses can't take away all of the options once players learn them. The offense dictates the action based on how the defense attempts to do so.
My point is that these offenses exist, and teams can be/have been successful in the half-court running them. Despite this, our half-court offense continues to lack rhythm and structure season to season. As much as I respect him, Coach Boeheim has always preferred the "simple" on offense, sometimes to the detriment of the "good." His philosophy seems even more pronounced the last few seasons. However, coaches can teach an offense with multiple actions that is still built on simple, fundamental concepts.
Still, to our Hall-of-Famer's credit, we have made two Final Fours since 2013 in spite of these offensive woes. Our coaching and defense can help us get to that level again. Unfortunately, a defense alone can't win a title. A better offense is the key to getting to the next level. A better offense with skilled players running it, that is.