The visit of a Fleet side who have not lost a league game since Boxing Day was Chester's first since boss Jon McCarthy was sacked following the 2-0 loss at Solihull Moors.
And they responded by producing a much improved display that yielded a point thanks to James Akintunde's 82nd-minute strike.
The result stretched the Blues' run without a home league win to a club record 15 matches.
But there were positives to take going into Tuesday's trip to Gateshead (7.45pm).
Shaw, who has stepped up from his role as player/assistant manager as the search for McCarthy's replacement continues, said: "We know we've done well with our recruitment, we know we've signed the right players, so to see them at full tilt was pleasing.
"It's been a tough week, we've lost a terrific man from the club who did a lot for all of us, and the lads were down.
"But to react how they did, how they trained on Thursday and how they played today, shows there's some tough, strong-willed men in there. I thought they were great.
"I think we had enough chances to win it. We lacked a bit of conviction and confidence in the box but Akintunde got his goal, he'll go on from that, and he deserved it for the work that he did.
"We were in control of the game for long periods, which is really pleasing. The lads got on the front foot and had a right go, which I asked them to do. They responded really well and I think they enjoyed playing this afternoon."
Shaw had particular praise for midfielder Paul Turnbull, who returned to the team in midweek following the passing of his father, and whose performance led to him being named in the Non-League Paper's Team of the Day.
"I thought he was outstanding," said Shaw. "I pulled him into the office before the game and I said to him if we were going to get a result today he was going to be huge as the other lads will fly forward with the licence that I've given them.
"He needed to do all the ugly stuff. He did that and he did more. He passed it well, he drove the ball on, he's a very good footballer, and hopefully this will kick him on and he'll have a very strong season."
Chester are aiming to have a appointed a new boss before the home clash with Maidenhead United on Saturday, September 23 with one of the managers who have an expressed an interest in the job, Dino Maamria, taking in the Ebbsfleet match from the stands.
That means Shaw's last two games in charge are likely to be the visits to Gateshead on Tuesday and then Dover Athletic on Saturday.
And the 30-year-old said: "I enjoyed the goal, I enjoyed seeing the lads work as hard as they did, and I enjoyed seeing bits we touched on on Thursday and before the game coming off. The worry is when they've got possession and when they're in and around the box. I don't think anyone can ever enjoy that.
"Everything does rest on my shoulders. I've had to step up probably five years before I ever thought I would like to do something like this but it's only for a week and I'm going to give it everything, and the lads have responded great."