Just because you 'can' tolerate pain, that doesn’t mean you should. Pain can subconsciously change the way you move, leading to tissue stress elsewhere and potentially additional injury.
If an exercise is hurting when you’re doing it, something is wrong. When the muscles are performing their respective functions adequately, there will be no pain, just the burn associated with lactic acid accumulation.
If you choose to work out through the pain, it is likely you will be making the situation worse, and probably not even working the muscles you meant to.
Pain causes a reflex inhibition of affected muscles, essentially shutting them down to avoid further insult to the body. They will fail to engage properly, leading to further compensation in order to perform the movement in question.
A much better strategy is to either find a way to modify the technique so as to keep it pain free or simply find an alternate exercise. The imbalances and compensations which likely led to the pain in the first place can be dealt with through my treatments and with appropriate corrective exercise.