The loss became historic for the Marlins, who have now been shutout for the first time in club history in three straight games.
The 27 straight innings matches Miami's longest drought in club history, initially set over four games from Sept. 11-15, 1993.
"It's kind of how our season is going," Johnson said. "It's something you never want to go through. These guys are trying to get hits and score runs. They're trying their best. There is nothing you can do."
Philadelphia's Kyle Kendrick, Josh Lindblom and Jonathan Papelbon combined to hand the Marlins their 13th shutout of the season, most in the National League.
The hard-luck loss went to Johnson (7-9), who was masterful after surrendering Rollins' fourth leadoff home run of the season.
"I made a mistake early on," Johnson said. "I can't do that right now, but you've got to keep going, keep battling. It was supposed to be away, but right down the middle."
In eight innings, Johnson scattered three hits, struck out seven and walked one.
Still the right-hander's 114-pitch effort was overshadowed by Kendrick, who gave up five hits while striking out six in seven shutout innings.
Actually, Johnson has been impressive over his last five starts. The right-hander has a 1.60 ERA (six earned runs in 33 2/3 innings. He is 2-2 in those outings.
After facing Los Angeles' Chris Capuano on Sunday and Cole Hamels on Monday, Miami manager Ozzie Guillen was hoping for a little of a break on Tuesday against Kendrick, who entered the game 4-9 with a 4.86 ERA.
"Our offense still couldn't get anything going," Guillen said. "I thought after the last couple guys pitching that today would be a little easier. I was wrong. I think we need to get better offensively and try to get something going. A lot of swinging and missing. We really, offensively, we have to step it up."
The game marked the big league debut of catcher Rob Brantly, the 23-year-old acquired on July 23 from the Tigers as part of the Anibal Sanchez-Omar Infante trade.
Brantly went 0-for-3, but he was praised for how he took charge and worked with Johnson.
"I was worried about him catching JJ," Guillen said. "The scouting report I think was a better indication that he's a hitter. ... He did a tremendous job. This kid, we're going to take it easy with him with teaching him how to handle at the big league level, but I like what I see.
"He had a great swing. Obviously he's a kid, and we got to polish him, but I like it because I was a little bit worried about how he would handle behind the plate. He did a tremendous job behind the plate."
Two pitches into the game, and the Marlins were in a hole they couldn't climb out of. Rollins launched a 91-mph fastball into the second deck in right field, giving him 14 homers on the season. It was his first career dinger off Johnson, and it came on his 36th career at-bat.
In the ninth inning, the Marlins made it interesting after Papelbon walked Carlos Lee with two outs. Gorkys Hernandez pinch-ran, and Giancarlo Stanton stepped to the plate. But the Miami slugger rolled a slow dribbler to second for the final out, giving Papelbon his 26th save.
Miami had a scoring chance in the first inning. Justin Ruggiano singled and advanced to second on Chase Utley's throwing error after he caught Jose Reyes' hard liner.
Kendrick got out of it by retiring Lee on a groundout to short.
"He was very aggressive in there," Phillies manager Charlie Manuel said of his right-hander. "That helped set him up for the rest of the game."
In the fourth inning, Reyes singled, giving him a hit in 30 of 31 games. But Reyes was caught trying to steal second. Lee followed with a single, but the inning fizzled.
In the sixth inning, the Marlins had Bryan Petersen reach third, the only time all game a runner advanced that far. Again, Kendrick wiggled out of trouble by getting Lee to pop out to Utley.
The Marlins last scored in the eighth inning on Saturday, when they beat the Dodgers, 7-3.
The Phillies have taken the first two of three in the series, and the Marlins are a season-worst 13 games under .500 (52-65).
Can Guillen pinpoint his team's struggles to score?
"Name it," the manager said. "Besides work. They work every day. I think they spend more time in the cage than they spend in the batter's box. They spend three hours in the cage and two seconds in the batter's box. It's kind of weird when you get in a slump together.
"The team can run a little bit, a guy can put a ball in play, but right now we got to get better offensively, because it starts getting old. It's not fun when you're not scoring any runs. It's not. You feel like you're flat, you feel like something has been missing. We got to get it going in that department."