The outcome was decided after Greinke left the game, when Ryan Schimpf hit a game-tying homer in the eighth and a game-winning homer in the 10th.
"We played a really good game," Greinke said. "We didn't pull it out, but it was a well-played game. I think we'll win most of them if we play like that."
Against the Red Sox everything Greinke threw seemed to wind up either in the gap or over the fence as he gave up nine runs on 10 hits in just 1 2/3 innings.
"Last start was just so bad I don't even know where to start," Greinke said. "I didn't feel like it was the worst game I ever pitched, but the results were definitely saying that."
That was what surprised Greinke the most about that day in Fenway was that his pitches felt good leaving his hand, but they certainly didn't fool the Boston hitters.
Did that make him a little more anxious for this start to finally roll around?
"Little bit more, yeah," Greinke said. "I just tried to make good pitches again today and try to just not think about the last one too much because it was so bad."
Greinke allowed just one run over the first three innings, but the Padres did hit some balls hard.
That reversed itself later in the game as he allowed a run in the seventh on some balls that were not hit particularly hard.
"It got better after the third inning," Greinke said. "I was getting hit pretty good especially, the second and third innings, and then made better pitches the rest of the way. Last inning I thought I made some decent pitches that they got hits on that maybe made up for some of the harder balls they hit earlier that we caught."
Greinke turned a 4-2 lead over to the bullpen after seven.
"He did a good job," D-backs manager Chip Hale said. "He battled and gave us a chance to win the game. That's exactly what the starting pitcher is supposed to do. He got us through the seventh, we're very happy with that."