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Kavanagh said the fight went somewhat as expected, particularly in the first round where he had prepared his fighter to expect to be taken down.
"The goal of round one was to get out of it still having energy," Kavanagh said.
"We didn't want to put a huge amount of effort in trying to get back up in round one, which seemed to happen many times with his other opponents and they kind of got back to the stool really tired.
"So round one, make him pay, do our best on the way in, fight as hard as we can — but if we do end up down, if it's against the fence because we expected it there, try and stay seated up, if we end up on our back, just try and play guard until the bell. Accept it will be a 10-9 round.
"For round two, again same plan. Do as much damage as we can, but if we end up on our back, don't put a huge amount of effort into trying to get back up (because) he's an absolute master of regrounding people.
"That turned out to be a 10-8 round, he got some good shots there and obviously he landed the great right hand. So that was a bit more than we hoped for."
But despite the punishment McGregor copped in the final minutes of round two, he bounced back in round three, winning the round on all three judges' scorecards.
"Round three things started turning a little bit in our favour," Kavanagh said. "(McGregor) did a lot better job of keeping it in the middle (of the cage), defending the take-downs.
"In the beginning the consensus was Conor knocks him out in the first — or Khabib takes over from round two on. For us to win the third round was probably a bit of a surprise for people.
"But the Al Iaquinta fight, if you look at that, from round three on he wasn't able to hit any take-downs. So we hoped that was how it would go in round three, we'd start being able to defend the take-down much easier and start landing our shots. And that did happen (but) not as well as we planned."
McGregor failed to do any major damage to Nurmagomedov in the third and then made a critical mistake after being taken down in the fourth.
"In round four he hit another great take-down," Kavanagh said. "(McGregor) made a mistake giving up the overhook, exposed our back and that was all she wrote."