Cummins was rested for Wednesday's final one-dayer and will also be missing the T20Is.
Part of the white-ball touring contingent to England in September, Cummins was in UAE then to play the IPL 2020 for Kolkata Knight Riders (KKR).
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The think-tank opted to give him some free time after winning the first two ODIs of the three-match series against the Indians. The 27-year-old will also miss the T20Is as part of his workload management before the Test matches.
"It probably wouldn't have been his call, he probably would have wanted to play, the players generally want to play," Lee told Foxsports.com.au.
"I would have thought after a couple of games they shouldn't be tired. I always found that for my rhythm personally that the more games I played the better rhythm I had," he added.
Australia's 13-run loss in the final one-dayer only highlighted Cummins' absence as Lee said he doesn't agree with the decision of resting the paceman when he is fit and performing.
"If I had a week's break, whether it be a break in the tournament or whether I was rested, it's almost like you've got to go back and find that rhythm again," he said.
"There could be a guy who is carrying a hamstring injury or a little niggle, shoulder might be a bit sore, and the best way to get them into their best preparation is to have a few days off.
"That's fine but if they're fully fit they should be playing."
Earlier, spin legend Shane Warne also slammed the Australian selectors and team management for resting Cummins from games played during the international summer. Warne asked whether the IPL, for which Cummins was fully available, is getting priority over national duty?
"I know it is a big summer that we have and it is pretty jam-packed, but I don't think Australian players should be resting after two games," he had said.
"Why are they resting? Is it because they played IPL? So they are allowed to go and play all these games in the IPL and then they need a rest because they have been playing in IPL?"
"Surely playing for Australia is more important than playing in the IPL. So I would say you should choose. Either miss the IPL or you cannot miss games because you need a break coming off an IPL for an Australian game," Warne added.
(Inputs from PTI)