The Reds have forced themselves back into the play-off places in the Sky Bet Championship after remaining unbeaten in their six matches during December.
Billy Davies' side stretched that streak to seven games on New Year's Day when they came within a whisker of a third straight win against Reading, only to be denied by an equaliser in the fifth minute of injury time.
By contrast, West Ham are without a league win in seven outings and have won only one of their last 13 Premier League fixtures - a run which sees the Hammers head to the City Ground on Sunday with just Sunderland beneath them in the table.
Despite the disappointment of conceding such a late goal at the Madejski Stadium, Paterson says Forest remain confident going into the third round tie.
"We will keep our heads high and look forward to the next game - and we will look to remain unbeaten," the 22-year-old told the club's official website.
"We have had some tough games, when you look at QPR, Leeds and Reading - and a couple more before that as well.
"We have collected seven points from three games in the space of just a week and we are on a good unbeaten run, which we need to keep going.
"We are looking forward to the FA Cup game, when we will be looking to add another win to the run."
Paterson, a B£1million summer signing from League One club Walsall, will be looking to keep his shirt against Sam Allardyce's side after making his first start in just over a month against Reading.
"I was happy to get through the 90 minutes, I just want to work hard," he said.
"It would have been sweeter if we had marked it with a win. But hopefully I did enough to be in contention for the next game.
"We have a good, big squad, so we will have to see what decisions the gaffer makes."
Another player hoping to start on Sunday is Simon Cox.
The Republic of Ireland international striker has been on the bench for the last two games, after missing the home win over QPR through illness.
But he is itching for a return to the side and the opportunity to test himself against Premier League defenders.
"I am fully recovered now," said Cox. "It was not nice to be ill over the Christmas period. I was in decent form and I wanted to carry that on, hopefully I will get a chance to do that.
"Obviously everyone is looking forward to it because West Ham are a Premier League team.
"If we get to the promised land of the Premier League next season then we will be going up against this sort of team every week, which is what we want."
Midfielders David Vaughan, on loan from Sunderland, and Djamal Abdoun will be checked on after both players were absent at Reading. Striker Darius Henderson will be available for selection after completing a three-match suspension.
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