That's a fair point, but the more often you get relievers up to warm up, the more you risk 'overuse'.
Price was cruising until the 8th inning. He was only at 89 pitches. There was no reason to have someone warming up to start the inning, 'just in case'. There was no indication whatsoever that Price wouldn't be able to get through that inning.
Now I agree that he should have gotten someone up after the single following the HR, and he could have used any number of stall tactics to get the reliever ready, but that inning did unfold very, very quickly.