The visitors went in front after 11 minutes through a fine strike from Neil Danns but that advantage was cancelled out in the 32nd minute when Tommy Smith acrobatically drew Ipswich level.
"We got better in the second half but didn't play particularly well," McCarthy said
"Bristol City did play well, though, and I should congratulate them. I was glad to get in at 1-1.
"I was happy to take a point from a game we could have lost, to not lose twice on the bounce and not to crumble when we could have done.
"In terms of performance, it was nowhere near as well as we played against Nottingham Forest or Millwall.
"But these are the hardest games. Expectations are higher when you play teams around you but, as today's results prove, this league is bonkers and it will be that way until the end.
"I've said it before but it will be a scrap until then. We've had a good run but I've seen it before when a new manager comes in.
"A team starts winning and everything is shiny and new, but it's about maintaining it."