Reds were 1-0 up thanks to Ashley Nadesan's strike before Lewis Alessandra popped up three minutes into added time to salvage a point for the home side. See the Carlisle United v Crawley Town match report here.
To add to the frustration, Nadesan missed a penalty in the second half.
The draw continues the Reds unbeaten start to 2022 but they were left frustrated by this point.
When asked to sum up the game, Bradbury said: "Disappointed. I think that shows how far we have come over the last month. They have been on a great run, Keith [Millen] has turned them around here.
"I thought we had the better spells in the game, more possession, certainly in the first half.
"We knew they were going to throw everything at us in the final 15 minutes, which they did and we defended great, but one switch off the lad gets free and scores a good header.
"I am gutted for the lads because they worked so hard for each other, very united and hard-working and that’s what we need, this is a league where you need those qualities."
And former Portsmouth striker Bradbury felt sympathy for Nadesan after his spot-kick miss.
He said: "I am gutted for Nadders missing that penalty, he’s been excellent up top leading the line.
"He deserved his goal but everyone misses penalties and we will back each other up, dust ourselves down go again. It keeps out unbeaten run going.
"In hindsight it’s a good point but when you are 1-0 up with two minutes left it’s a frustrating one.
"The whole dressing room feels like a loss, we have got to be positive with how we come and did what we did."
But Bradbury was full of praise for the the travelling 76 Reds fans. He said: "I want to thank all the fans who came up from Crawley. It’s a hell of a long way to come.
"Hopefully they are seeing that the team are absolutely 100 per cent together and working hard for each other today."
Tilley said: "Before we come here we would take a 1-1 draw away at Carlisle, but it’s heartbreaking at the end to let in a 91st minute equaliser. It feels like a loss. It’s a point and and carries on the unbeaten run."
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