Exactly. The cheating caused them to play with one hand behind their backs, apparently. I think the videotapes caused them to overanalyze their opponents. Now that they don't cheat anymore and focus on their own play, they have become the most dominant team in the history of the NFL. Apparently the cheating cost them at least one or two Super Bowls.
The NFL did a huge favor to Bill Belichick by making him focus more on his own team instead of the other teams. They made him realize he is even more of a genius than previously thought.