Daniel Farke admits bottom club Norwich must win five of their seven remaining games to stand a chance of pulling off a remarkable Premier League great escape.
The Canaries are running out of time to preserve their top-flight status and sit six points from safety going into Wednesday's game at Arsenal.
City boss Farke has seen his side win only five times in the league all season, while they have lost each of their three post-lockdown matches, including being knocked out of the FA Cup following an extra-time loss to Manchester United at the weekend.
The German described the task of scraping survival as "doable" but accepts it would be an "extraordinary" achievement.
"We are not naive and we know that we have to win probably five out of last seven games and this is a huge task," said Farke.
"It would be outstanding and something extraordinary if we can handle this.
"Once you are there with a draw against Man United after 90 minutes and you were actually the better side, that says a lot about you are capable to be successful against each and every team.
"As long as you are capable to do this then you can also win games on this evidence.
"We know that there is a bit of pressure on us in terms of delivering with results. We are not naive but we still have a chance.
"It is difficult but it's possible and doable.
"Performance-wise we are heading to the right direction and if we can go further this way, I'm pretty sure we'll win definitely a few points in the last games, hope we can start with a win tomorrow."
Norwich have endured a season of struggle since clinching the Sky Bet Championship title last year.
Farke has been reliant on a fairly inexperienced squad, rather than bringing in big-money signings, and suffered numerous injury problems.
Despite relegation seeming extremely likely, the 43-year-old is confident he retains the backing of City's board.
"I know that I'm in an unbelievably privileged role," he said.
"I can't ask for a better relationship to a sporting director (Stuart Webber), I can't ask for better owners, I can't ask for a better relationship to our board.
"Also, to our supporters, who are there with so much trust in the good times and the bad times.
"I'm unbelievably thankful and grateful for this. On the other way, they also know they have a head coach who is not complaining and just crying and asking to spend more money.
"I totally accept we went into this season with a bunch of young lads and some players who have never played on this level.
"Our relationship is full of trust. I can't ask for better people to work with."
Norwich will be without suspended defender Timm Klose at Emirates Stadium following his sending off in the loss to Ole Gunnar Solskjaer's side, while Lukas Rupp (hip), Max Aarons (calf) and Adam Idah (quad) face fitness tests.
Moritz Leitner will miss out due to a hernia problem but Todd Cantwell is fit to play following an abductor issue.
