"We could have gone through the playoffs," Davis told ESPN's Rachel Nichols. "No one could really stop us as bigs. We go to the Finals if we went."
Cousins suffered a ruptured Achilles tendon at the end of January and will miss the remainder of the season.
Like Davis, Cousins was named an All-Star Game starter after an outstanding start to the season. The former Kings star finished the year averaging 25.2 points, 12.9 rebounds and 5.4 assists per game in 48 appearances.
The Pelicans were 27-21 with Cousins in the lineup, but they have gone 4-5 without him. They enter the second half of the season as the Western Conference's No. 8 seed, but they hold only a half-game lead over the Los Angeles Clippers for that final playoff spot.
While losing an elite player is bad enough, Cousins' absence also puts extra pressure on Davis.
"When he goes down, it's, all right, it goes back to AD before DeMarcus, a lot of minutes, weight of the world on your shoulders," Davis told Nichols. "You know, you gotta carry the team on your back, you gotta almost get 40 every night for us—to give us a chance to win."
Davis is averaging 27.4 points and 10.7 rebounds per game this season, so he is clearly capable of carrying the Pelicans. However, New Orleans lacks scoring depth beyond him, Jrue Holiday and E'Twaun Moore.
With the team currently facing 200-1 odds to win the NBA title, per OddsShark, the loss of Cousins could prove too much to overcome.