Considine's late headed goal helped 10-man Aberdeen to victory at Motherwell last month, setting up a League Cup semi-final against St Johnstone.
Considine said: "I felt strongly this year a lot of the younger members of the squad have grown up this year.
"I think that's with playing every week and having confidence instilled in them from the manager and Tony (Docherty) and I feel it's given us a real determination and confidence and it's shown in the league and we just need to keep doing that in the cup.
"I think it epitomised what we're all about when we played Motherwell with 10 men and to keep going to the very end."
The 26-year-old spelled out what it means to bring some cup success to a club who have not won a trophy since the 1995-96 season.
"It's massively important for a club like Aberdeen," the centre-back said. "We want to get as high as possible in the league but I feel we owe ourselves, the club and the supporters a good run in the cup.
"It would be great to win a cup this year.
"The confidence is high within the squad. I feel we have the players to do it this year but full respect to Partick Thistle on Sunday.
"It's going to be a really tough game but if we go into the game in the right frame of mind we can hopefully come up the road with a win."
Considine brushed off the importance of their recent 3-0 and 4-0 Scottish Premiership victories over the Jags.
"When it comes to cup games it's completely different," he said. "Whichever team turns up on the day and wants to win it most will win.
"Both games have been very open. They play some real good football and have some good players going forward. So it will be good game of football."
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