Adams had not fought for 11 months and showed clear signs of ring rust on her return to action.
Salinas clearly felt she had won the fight, but only one judge gave it to her by the score of 96-94.
Another judge scored it 97-93 to Adams, with a third seeing it as a 95-95 draw.
There certainly appeared to be sympathy for Salinas judging by the reaction of some of the crowd at the famous London venue.
"I was a bit ring rusty," Adams told BT Sport 1.
"It was not the result I wanted and if she wants a rematch I'd be happy to go again.
"I've got this one out of the way and I've still got the belt."
Adams made a confident start as she was first to the punch and Salinas, four inches shorter than the Leeds boxer, struggled to get within range.
It was one-way traffic in the first three rounds, but Salinas was undeterred and dominated the fourth session.
The Mexican kept moving forward and catching Adams with crisp shots in the second half of the fight, although in the end it was not enough to take the title.