The Scotland international has started all five games under new boss Dean Smith.
The 20-year-old was unable to help the Canaries avoid a second consecutive defeat on Saturday after a Cristiano Ronaldo penalty consigned them to a 1-0 loss at home to Manchester United.
Norwich have little time to dwell on the result with Aston Villa due to visit on Tuesday and despite remaining at the bottom of the table with a lengthy list of absentees, belief is growing under new boss Dean Smith
“We will take real confidence from this game into Aston Villa. We know we can give them a good battle and take three points,” Gilmour said.
“We have had a couple of people unwell and injuries but there is a real belief there in the changing room.
“We know we are a good team, we can see that and we are building every time we play. I know the results aren’t quite there yet but I am sure we will get a good run soon and we want to keep going.
“This is what we’re here for, to stay in the Premier League and there is a good enough squad in there to do that.”
Captain Grant Hanley (shoulder) is set to become the latest player on the treatment table with Ben Gibson, Andrew Omobamidele, Mathias Normann and Milot Rashica among those unavailable for the United clash.
It was another blow to ex-Villa boss Smith but his decision to bring Gilmour back into the fold since his arrival last month continues to be vindicated.
The Chelsea loanee has started all five matches under the new boss and impressed following a spell on the sidelines under Daniel Farke, who was sacked at the beginning of November.
Gilmour added: “I love playing and working under the new manager. I think he has been really good with me so far.
“I just need to make sure I am putting in good performances to make sure I am playing every week.
“It is a good squad in there, who are fighting for places and injuries are building up so I need to make sure I am on it every day in training to get the opportunity. Boys are excited, they want to do well and stay in this league.”
Smith and assistant Craig Shakespeare have made subtle changes since they took over with the warm-up tweaked and Norwich more direct on the ball.
After starting their tenure with a three-game unbeaten run, the division’s basement club have lost their last two matches to Tottenham and Man United but Gilmour is positive points will start to come.
“Of course the new manager wants to come in and put his own stamp on things with how he wants us to be,” the Scottish international added.
“Everyone is different but working under the manager here so far he has been really good on the training field, making us more compact and tougher to beat.
“I am you can see that on the pitch. We are not wanting to let teams have their opportunities and we are creating a lot more as well. We are quite direct, so I am enjoying it. I am sure it will click and we will get the points soon.”