Bidding for his ninth victory on the U.S. circuit, the long-hitting Johnson closed with a five-under-par 66 in the final round at Riviera Country Club to finish alone in second at 13-under 271.
A birdie at the par-four 15th put Johnson just one off the pace but he was left to rue a birdie chance that went awry at the par-five 17th where he found the left rough off the tee and then hit trees with his second shot.
Still in the left rough some 90 yards from the flag, the American hit a wedge to 45 feet from where he two-putted for par.
"I just hit a poor shot," Johnson, 29, told reporters of his second on 17. "I had a great look at the flag, I just kind of pull-hooked one.
"For me, I've got to keep it a little left because you can't drive it in the bunker," he said of his tee shot on 17 where he had to avoid a fairway bunker on the right. "But I was fine there."
Johnson had been one of four players tied for the lead early in the final round but was unable to keep pace with fellow American Bubba Watson, who piled up seven birdies in a flawless display to triumph by two shots.
"I'm playing good," said Johnson, who tied for second at last week's Pebble Beach National Pro-Am where he also closed with a 66. "I'm not playing great but I'm playing good, solid.
"Today I played really solid, hit some poor shots but I was able to save pars on those. Coming down the stretch, I thought I hit a lot better shot on 16, ended up just short in the rough and had to make a pretty good up and down just to save par.
"But you know, when you shoot 14 under on the weekend, it's tough to beat that."
Watson did exactly that, closing with successive scores of 64 at Riviera as he went bogey-free over the weekend to claim his fifth title on the PGA Tour.
Asked whether he had any regrets about his week after he seized the first-round lead with an opening 66, Johnson replied: "The golf course, even with not a lot of wind, it still plays tough. With the greens firm and fast, it plays very difficult.
"I just really didn't hole the putts that I needed to on Friday and Saturday, but today I did. Just got to make those short putts. Friday and Saturday, I didn't do that, but Thursday and Sunday, I did.
"And I was still right there with a chance to win," added the American who has finished no worse than joint sixth in his first four starts on the 2013-14 PGA Tour, including victory at the WGC-HSBC Champions in November.