Ian Desmond took care of the offense by driving in both runs, drilling a homer in the second and adding an RBI single in the fourth off Phillies starter Kyle Kendrick.
Due to the shaky ninth inning, though, Johnson admitted that he's rethinking how he'll use his bullpen in save situations moving forward.
"It's frustrating," he said. "I have all the confidence in the world in [Rodriguez]. He's got great stuff. Sometimes he tries to do too much and gets a little excited out there. It's not easy. He came a long way last year and he's come a long way this year. But he's not quite there to be a polished closer."
Asked if he could continue putting himself in a position where he had to have another reliever warming up behind his closer, Johnson indicated that he couldn't.
"I'm going to sleep on it, but I'm going to look at alternatives," Johnson said. "Henry's either lights out or sometimes he's exciting. I was hoping the first four hitters we'd get a couple outs. I wanted to get by the two big right-handers on their bench [Wigginton and Hector Luna]. But I had no choice the way it was going. I had to go get him and let [Burnett] face the right-handers. Not that he can't get right-handers out, but it wasn't what I wanted to do.
"I have confidence in everybody out there, so I have a lot of alternatives. It may just be by committee, and who's rested at the time goes ahead and pitches the ninth instead of the eighth."
One of the alternatives could be Burnett.
"I'm just going to do whatever they ask me to do," he said. "That's the way I've always been. Henry's been good all year. He's just had a little hiccup here the last couple weeks. But any time you can help your teammate out, that's what we're here to do.
"The biggest thing is you have to come in and throw strikes. As a closer, your lead is going to be three runs at the most. His stuff, he's just got to get the ball over the plate, and good things will happen. He's just in a little funk right now. He'll get out of it. He's too good not to. In the meantime, we'll do whatever we have to down there until things get better."
Another option could be right-hander Craig Stammen, who blanked the Phillies in the seventh and eighth Monday night.
"I'll leave that up to them," Stammen said. "I [closed] in college and it was fun, but I don't think I've quite earned it yet."
There are three factors that have made this an issue for the Nationals. One is that Drew Storen is on the disabled list with elbow soreness and Brad Lidge is recovering from hernia surgery. Both are expected to miss about three more weeks. The second is that Rodriguez, who left the clubhouse without speaking to reporters, has two losses, two blown saves and a 10.50 ERA in his last eight appearances.
And the third is that Gonzalez was dominant, but he needed 108 pitches to get through his six innings. That meant Johnson had to turn the game over to his relievers earlier than he would have liked.
Gonzalez improved his record to 6-1 and lowered his ERA to 1.98. But that came at a cost.
"Gio pitched a heck of a ballgame," Johnson said. "The only thing that bothered me is that he threw a heck of a lot of pitches. He was pretty much unhittable, but his pitch count was way up there. And our bullpen was kind of short. I'd prefer he didn't have as many strikeouts and fewer pitches so he could go further. He's got such great stuff. I'd prefer to see him get into the seventh or eighth inning. Sixth inning puts a crimp on my bullpen."
Johnson sighed and then smiled.
"The outcome was good, but getting to the outcome wasn't that easy," he said.