The visitors battled for their Premier League lives but are now staring relegation in the face as they are two points behind 17th-placed Sunderland, who have a game in hand and a better goal difference.
Norwich's last game of the season is against Arsenal at Carrow Road but they could be relegated in midweek if results go against them, with Sunderland taking on fellow strugglers West Brom at the Stadium of Light on Wednesday.
Chelsea struggled to build up any real momentum on Sunday, and although Andre Schurrle and sub David Luiz both hit the woodwork with strikes, Norwich could arguably have earned three precious points if they had been awarded a first-half penalty.
Martin Olsson burst into the 18-yard box and was felled by John Terry after nudging the ball past Chelsea defender Ashley Cole - but referee Neil Swarbrick turned down the Norwich appeals, much to Adams' dismay.
Adams insisted the point was well-earned, though, and ensures they are still fighting for their top-flight survival.
"The point has kept us going for sure - I thought the performance was outstanding," the Norwich boss told Sky Sports.
"Defensively we had a gameplan and we've virtually executed it to perfection.
"I can't speak highly enough of the players - the performance today from the first minute to the 94th was so strong and solid.
"Of course we would have liked to posed a few more problems for Chelsea, but we're playing against one of the top teams in Europe here.
"You've got to gain a foothold in the game and I thought we did that - and we nearly caused a surprise in the end.
"I felt we had a stonewall penalty in the first half, which had we been given could have got us two more points.
"I'm not biased, I have had a look at all the claims, and I don't think the Chelsea ones are penalties, while I think ours is stonewall.
"Just looking at it, I think Martin (Olsson) has been taken out by John Terry. He got the first touch past Ashley Cole and it looks like John Terry has just cleaned him out, which for me is a stonewall penalty."
Adams sent on Nathan Redmond for lone striker Johan Elmander in the second half, leaving strikers Gary Hooper and Ricky van Wolfswinkel on the bench.
Redmond's pace caused problems for the Chelsea defence, and Adams said: "It's finding a balance. What you don't want to do is give the game away as if we'd have lost today, we'd have been relegated virtually.
"I thought Johan was excellent for us, holding the ball up, causing a problem and just giving us some breathing space in the first half.
"He had to come off as he was shattered after putting in a great shift. That was the time to try and test John Terry and Gary Cahill with a bit of pace. The game was opening up a bit then so we felt that was the right time to try and get Nathan round the back and it nearly paid off.
"We're watching other games now and what we hope is that we go into the Arsenal game on Sunday with an opportunity, because with the type of spirit and commitment we saw today we'll have every chance."