Roared on by a vocal away support of nearly 4,400 fans at the Macron Stadium, McCall's men more than held their own against another of Sky Bet League One's early pace-setters.
With former City boss Phil Parkinson in the dug-out for the hosts, Bolton arguably edged the opening period but City looked the more purposeful side after the break.
McCall's side enjoyed a greater share of the ball in the second half and looked the more likely to engineer a breakthrough but they weren't quite able to find a way through Bolton's structured defensive line.
Speaking after the goalless draw, a result that keeps City fourth and three points off top spot, McCall said: "I think it is a fair point.
"We have to remember that Bolton undoubtedly will be up there and they have a lot of players who have played at levels higher than this one.
"I'm just a bit disappointed that we didn't quite create as many chances as we would have liked. Having said that though, we kept going and trying to score even in injury time.
"You know you are going to come under a lot of pressure here at Bolton, a lot of balls into your box, but there were some huge performances from us today (Saturday).
"They are a large and physical team and they had a few inches on us when marking up for set-pieces but I can't really remember them having a chance from a first or second ball.
"The lads showed tremendous determination to defend properly and to do their job. They also showed courage to keeping getting on the ball and play.
"We had some good spells in the second period and we had some opportunities where we maybe should have got our shot away quicker.
"We have a tremendous group of lads in our dressing room and a superb backing from the supporters in the stands as well. We just have to be a little bit more clinical in that final third to break teams down."
Following this Saturday's hard-fought draw at Bolton, City's thoughts now turn to their home encounter with Fleetwood Town on Tuesday evening.
McCall says Josh Cullen (knee) and Nicky Law (thigh) will need to be assessed following knocks picked up against Bolton, while James Hanson and Tony McMahon are set to miss out again after being sidelined for the trip to the Macron Stadium.
McCall continued: "At half-time it looked like Josh might have to come off but he is a little lion and he wanted to stay on.
"How he'll be tomorrow (Sunday) once the adrenaline wears off and he's slept on it we're not too sure. We'll have to monitor him.
"Hans (James Hanson) got a bang on his calf last week and that unfortunately hasn't settled down as we would have liked. He will probably still be a doubt for Tuesday but we'll be more hopeful for next Saturday (away to Chesterfield).
"Tony has been back training with us now for two weeks or so since his original injury but he just clipped a ball down the line during training on Thursday and felt his thigh go again.
"That is something we will need to look into because he's been back in training at a good speed for a while now and looking to get back into the side before this happened.
"Naturally, he is frustrated by this set-back and I would have thought he'd be out a bit longer than Hans."