While Michael O'Neill's side go into the match with three draws from their first four matches, Group F leaders Russia boast a 100 per cent record and have yet to concede a goal.
At 97th in the world, O'Neill's men are also a massive 87 places below their opponents in the latest FIFA rankings.
But former Manchester United keeper Carroll does not see why his side cannot hope for the best.
The last two matches at Windsor Park may have ended 1-1 against lowly Luxembourg and Azerbaijan, but the 35-year-old is eyeing a memorable night.
"We want to win every game, We are not happy with a draw or a 1-0 defeat, no matter who we play," he said.
"I'm from Northern Ireland; we hate losing.
"Of course we want to win. We must have had about 50 shots against Luxembourg and Azerbaijan without getting the goals we deserved.
"The players are really up it for even though Russia have such quality players.
"We most definitely have to get a win to keep our hopes alive. We have been doing okay but the two draws at home have not been good."
That Carroll is even in Belfast this week is something of an achievement for the well-travelled stopper.
After leaving Old Trafford in 2005 he embarked upon a nomadic career that took in brief spells at West Ham and Derby followed by Danish outfit Odense and Greek sides Crete and Olympiacos.
He also spent six years in the international wilderness, but was recalled by O'Neill and is now the undisputed number one for the first time in his Northern Ireland career.
That journey perhaps explains his optimistic streak.
"After what has happened in my life, I will keep believing in everything," he said.
"It is nice to be back in the squad. Six years away is a long time but I have been really impressed with Michael and (assistant manager) Billy McKinlay.
"We have a good mixture of younger lads and experienced players and the improvement is there for all to see.
"Everyone turns up and wants to work hard so things have changed for the good.
"It's going to be important to have the crowd behind us tomorrow and we will need them.
"If we show what we are about and give everything for the Northern Ireland shirt then I know they will be behind us."
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