They were sort of down to duress. The bench players that afternoon were Bryce Brentz, Aaron Hill, Sandy Leon, David Ortiz and Hanley Ramirez
It all happened in the 6th:
Hill hit for Brock Holt and doubled. Later in the inning, Brentz was announced for David Price. The Dodgers changed pitchers and David Ortiz hit for Brentz, drawing a walk. Betts singled Ortiz to 2nd (he was the tying run). At that point, Farrell wanted to run for Ortiz to try and tie the game up, so he used Wright with the bad result we all know.
So at that point, it was leave Ortiz on, use your other catcher or send Hanley in to run and lose his bat for later (and the pitchers spot was due up one more time)
The screw up was not using a pitcher for the role, but in using a guy who never runs the bases. Pomeranz, having just come over form the NL, was far more experienced in that regard, and had, as someone pointed out, pinch run a couple time earlier that year with the Padres plus run the bases as a hitter. I can't remember if Kelly was on the roster at that point, but he would have been a possible choice as well.