Warriors trailed 37-10 after 60 minutes last Saturday before scoring three tries to secure two losing bonus points in a 40-34 away defeat that kept them top of the URC.
"It was probably a rollercoaster of emotions in the dressing room," Carolan admitted on the BBC Scotland Sport website.
"I'm not saying at half-time we were out of the game, but certainly at 37-10, you're probably thinking the worst. but in our group, we know we've worked extremely hard.
"Last week we had a theme - to use the rodeo term - of just staying on the bull for as long as possible. We knew we'd finished the game strong, but unfortunately we had a massive 27 points to try and claw back.
"We just ran out of time. If we had another five minutes, we probably could've got another score. We're never happy to lose a game, but the strength of character, the camaraderie and the fight for each other, that togetherness and cohesion and willingness to work hard for each other and keep fighting for the jersey, that was evident in that last quarter."
Warriors had to contend with the altitude at the Loftus Versfeld Stadium - 1350m above sea level - as well as the temperature - 30C in the middle of the day.
"The conditions, the altitude, the team we played against, they're unbelievably physical - they're all challenges that are maybe new for us, but I thought we certainly rose to the challenge in difficult circumstances," added Carolan.
"It sets us up nicely for this weekend against a very dangerous Lions team - similar conditions, very physical. We can't try and chase the game too early.
"We know that five points this weekend, and five points against Zebre, would guarantee us top spot, but we can't be thinking about those things at the start of the game. We've got to let our processes look after themselves."