Whether that changes before the Crimson Tide play the Seminoles in the season opener remains to be seen, though, according to the head coach.
"I don't think we're an elite team right now," Saban said following A-Day. "I think we're an adequate team.
"But I don't mean that in a negative way. We come out of the spring a lot of years an adequate team. It's how you respond."
A-Day proved a mixed bag for the defending SEC champs.
On the one hand, starting quarterback Jalen Hurts and backup Tua Tagovailoa combined for 614 yards and five touchdowns through the air. But on the whole, the offense threw four interceptions and gave up 12 sacks.
The defense made as many big plays as it gave up, surrendering completions of 38, 47, 60 and 65 yards.
Saban said he expects to watch the game film Sunday and not feel satisfied with any position group.
"These statistics are very misleading," he said. "If you want to get the true stats on the passing yards, take away the sacks because those are the negative plays we had when we were passing the ball."
Nonetheless, Saban had to be pleased with the progress his passing game made in one area in particular -- the deep ball. After struggling to move the ball downfield late last season, he saw both Hurts and Tagovailoa taking shots deep with good success.
Star junior Calvin Ridley had a robust 102 yards and a touchdown on four receptions and true freshman Jerry Jeudy burst onto the scene with a team-high 134 yards and two touchdowns on five receptions.
Harris' team ultimately lost the scrimmage, though, as the White team beat the Red team 27-24 on a last-second field goal by JK Scott.
"These guys have been through that situation and now we have a chip on our shoulder," he said. "I feel like we're going to work even harder with the fact that we've been through that. We understand the situation we were in, and I just hope that we learn from it and get better."