Motherwell battled well and restricted Celtic to relatively few chances yet still came away from Glasgow's east end with a 3-0 defeat after Celtic goals by James Forrest, Albian Ajeti and Christopher Jullien.
Carson said: “We came here with a game plan to frustrate them, but they got the goal on the break and that was disappointing because that’s what we had worked on.
“Celtic do that a lot, they win the ball deep and they counter-attack on you.
“After any defeat it is disappointing, but I just felt that coming here and not making them really have to work for their goals makes it even more disappointing.
"When you come to places like this, you have to have that belief.
“I’m only speaking for myself, I can’t speak for the other boys, but I definitely came here with the impression we could get a result.
“You have to be brave on the ball and at times they did give us possession, but I don’t think we made the most of it.
“Listen, when you come to a place like this against a team like this, you’re going to be under pressure and you’re going to have to defend, and I think for long periods we did do it well.
“There were one or two lapses though and they punish you.”
Motherwell - winless with just two points from their first six games - will remain bottom of the table for at least a fortnight as, due to the international break, their next game is at home to St Johnstone on Saturday, September 12.
Carson said: “You could look at it both ways, maybe a break will do the lads good and we’ll come back refreshed.
“On the flip side, I wish the St Johnstone game was tomorrow and we could go and get that first win.
“We’ll have to wait two weeks and it’s disappointing to look and see that we’re bottom of the league.
“You have to take it on the chin, it’s where we’re at and we’re not going to turn it round by feeling sorry for ourselves or thinking about ‘we could have won that game, or could have won that other game.
“We’re bottom of the league and it’s on us to go away, come back refreshed and start climbing the table.”