The result leaves Spurs' top four hopes on a knife edge.
"We knew it would be tough," Adebayor told the Spurs website. "We needed to win and they needed to win to keep out of relegation.
"They scored a deflected goal in the first half. What could we do about that? Nothing.
"We dusted ourselves down for the second half because we knew we had the ability to come back.
"We showed character in the second half, played together, worked hard and went home with one point."