Yannick Bolasie's 84th-minute strike earned Argyle a share of the spoils at Brunton Park after James Berrett had given the hosts a first-half lead.
Reid said: "We played some decent football but their keeper made a couple of excellent saves and our final ball could have been better, we just didn't deliver.
"The players kept going and it's a difficult place to come because Carlisle are a good team. We deserved something out of the game, possibly all three points.
"Carlisle responded after losing 6-0 at the weekend and, all in all, I am happy with the way our players have gone about the job.
"It was a decent performance but if you don't get the final ball right you are going to struggle. We got caught by a sucker punch but their keeper had more work to do. Yannick had a shot pushed on to the bar and it was a great header for the goal."
Source: PA
Source: PA