Smith, 32, put up a courageous display but the 35-year-old Abraham grew stronger as the fight progressed.
Abraham won on all three of the judges' scorecards - 116-112, 117-111, 117-111 - to end Smith's hopes.
Smith was outpointed by Abraham in a far more controversial decision last September in Kiel, Germany.
"I felt I left it all in there tonight, I'm not going home with any or many regrets," said Smith, who now has 35 wins and five defeats from 40 professional fights.
"I've held my own more than enough with a quality world champion. He's only behind Carl Froch in the super-middleweight division and I believe I beat him the first time. But he beat me this time."
Smith came out on the front foot, landing with the jab and possibly taking the first round, after which Abraham slowly assumed control.
Smith's legs were made to sag in the fourth after a right hook from the champion but Abraham did appear to be affected by a Smith body shot in the sixth.
However, Abraham became more and more relentless as the fight wore on and Smith already needed a knockout with three rounds remaining.
Smith was wobbled by a big right hand in the 10th, after which the champion coasted the final two rounds.
On the undercard, Liverpool heavyweight David Price continued rebuilding his career with a sixth-round stoppage of Brazil's Irineu Beato Costa Junior.
Afterwards, Price, who was knocked out twice by American Tony Thompson in 2013, called out Manchester's Tyson Fury, although Londoner Dereck Chisora might be a more realistic option.
"It's time to go home now I think," said the 31-year-old, who now has 19 wins from 21 pro fights.
"I've lost twice, I've got nothing to lose and a man with nothing to lose is a dangerous man.
"Tyson Fury deserves a shot at the world title and I hope he gets it but if he doesn't and he's looking for an alternative in the UK, the biggest fight out there for him is me."
Also on the same bill, Leeds featherweight prospect Josh Warrington stopped Nicaragua's Edwin Tellez in the fifth round to improve his record to 20 wins from as many fights.
Warrington's next fight is against Puerto Rico's Dennis Tubieron in Leeds on 11 April, after which promoter Eddie Hearn will look to manoeuvre him into a world title contention.
Germany's Arthur Abraham enjoyed a convincing points win over Liverpool's Paul Smith in their WBO super-middleweight title rematch in Berlin.