The 5-3 win sent Kean's side to the top of the table, although it did look as if they had blown it earlier in the game.
Rhodes scored twice and there were further goals from Nuno Gomes, Ruben Rochina and even Scott Dann got in on the act.
For the home side, Albert Adomah had given Derek McInnes men an early lead, they also had Stephen Pearson and Sam Baldock on the score sheet, which lead to Kean having to admit that his side have some defending practice ahead of them.
Kean told Sky Sports: "It wasn't just the way he took his goals. I don't think he gave the ball away all afternoon and his link-up play was excellent.
"The great thing when you buy a quality striker is that when he gets a chance you expect him to score.
"But there is much more to Jordan's game than finding the back of the net and he is open to plenty of improvement at such a young age.
"It's great to be top of the Championship, even this early in the season, but it goes without saying that we need to improve defensively.
"We should have more points because we scored three at Leeds and only got a draw. It's our goals-against column that needs working on.
"But tonight we can enjoy an excellent win over a very good Bristol City team, who will take a lot of points home and away this season."