The visitors performed creditably to end a run of five consecutive defeats but Sunday's Stamford Bridge result still leaves them facing the likely prospect of Championship football next season.
To avoid such a fate, Norwich must hope Sunderland lose their remaining home matches against West Brom and Swansea City, while themselves beating Arsenal on the final day.
Chelsea boss Jose Mourinho questioned Norwich's conservative tactics in light of their grave situation, but Adams was pleased with how his players stuck to instructions.
He also pointed to a rejected first-half penalty claim, when Martin Olsson went to ground under challenges from Ashley Cole and John Terry, that might have paved the way for three priceless points.
"I'm immensely proud," Adams said. "I thought it was a phenomenal performance.
"We had a game plan and the players executed it virtually to perfection.
"I would have liked a little bit more attacking threat from us as a team. Chelsea had a lot of possession and put us under a lot of pressure.
"Had we done that then who knows?
"I thought we had a stonewall penalty denied us in the first half. Had we got that then maybe we'd be going away from Stamford Bridge with three points instead of one.
"But in terms of the players’ effort it was fantastic."
As for Norwich's prospects of survival, Adams is realistic but believes his players can affect their fate if given the opportunity next weekend.
He added: "We've got to keep our fingers crossed now and hope for a few results but if we go into the last game of the season at Carrow Road against Arsenal needing to win the game… that's all we can hope for.
"I think you've seen today that if that's the case we'll give it every go. We'll be ready for it."
