After some resolute defending from the Canaries in the first half, the Gunners broke the deadlock with a stunning volley from Aaron Ramsey in the 53rd minute before Carl Jenkinson sealed the victory for the away side.
With West Brom's superior goal difference, Adams was aware Norwich would be facing a near-impossible task to remain in the Premier League.
"It was very difficult," he said. "We knew we were relegated before the game and the supporters were fantastic, we just wished we could have done better.
"I thought we did okay. We were a bit flat, understandably so, and for all our decent defensive work we were punished, we were lucking for more but it wasn't there.
"It's been desperately disappointing, it's been hard to take, but the performances haven't been good enough over the course of the season."
When questioned about his future at Carrow Road, Adams admits he remains unsure whether he will be leading the club in the Championship.
He said: "I have no idea if I'll be in charge (next season), it's up to the board and the chief executive, but that decision will be discussed in the meeting on Tuesday.
"We've got to try and pick the players up, this club needs to be a Premier League club and the players that are here will need to pick this club up back to where it belongs."