If we are talking about slams, I beg to differ.
There was a profound difference between Djokovic of 2011 and the years after. Djokovic didn't need to win a lot of close matches to win slams in 2011. What close matches are you talking about?
AO 2011- Dropped 1 set. Steamrolled Berdych, Federer, and Murray in straight sets.
FO 2011- He got to the SF without much issues. Federer just barely took him down.
WIM 2011- Was pushed to 4 sets in a few rounds, but never did it look like he would lose that final. He beat Nadal convincingly
The SF against Federer at USO 2011 was the only bullet Djokovic had to dodge at the grand slam level in 2011. After that, he took down Nadal in 4.
Your statement is only accurate if we are talking about masters events, as Djokovic edged out many close matches in those events. 2011 was a masterpiece year for him and is in no way similar to all subsequent years he has had.
2012 was when life got very difficult for Djokovic, but I think it had more to do with his rivals stepping up their games. Murray hired Lendl, Federer gained a lot of confidence in the 2011 indoor season and brought his A game to Wimbledon, and Nadal lost his Djokovic complex after the AO 2012 final. It was the perfect storm for Djokovic's downfall .