The striker who scored 33 times last year snatched the winner two minutes into stoppage time to seal the three points for the visitors.
Adams said: "We created a chance for him and he stuck it away and is back to his old self."
Pope's performances this term have been affected by a wrist injury, but Adams said: "Tom was outstanding and gave their centre halves a real torrid time and he is getting his rewards.
"If we can get enough decent balls into him he will score goals."
Adams was also pleased with his side's clean-sheet at Brunton Park, adding: "We had a bit of luck late on when their fella blazed over the bar and we will have stiffer tests.
"It was an important game for both teams. We wanted a clean sheet and the lads at the back did all the right things at all the right times.
"Winning breeds confidence and gives the players belief as well as sending supporters home happy. I thought we deserved that. As the game developed we wanted to go and win it and put on three more attacking players and went for it. The three lads had an impact on the game."
Pope swept the ball home from 12 yards after Carlisle had failed to cut out a ball from the right just minutes after midfielder Brad Potts had scorned a massive chance for the Cumbrians, scooping the ball over the bar from inside the six-yard box.
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