Roy Hodgson fears Crystal Palace could be even deeper in relegation trouble following their next three matches, after his first game in charge failed to have a "magic-wand effect".
A 1-0 loss to Southampton means the Eagles are the first club in top-flight history to lose their opening five games without scoring.
They travel to both Manchester clubs next, before playing Chelsea at home.
"It could be an even worse scenario when that spell is over," said Hodgson.
"But we'll work hard and if there are points to be won then we'll get them. We won't be lying down but, realistically, when you look at these three games, people will say 'how can you win them?' That's up to us.
"We won't be the first team to have a disastrous start and to pull ourselves out of trouble."
'The criticism will add up'
Palace fell behind in the sixth minute at Selhurst Park as Steven Davis' goal for Southampton ensured the former England manager's reign at his new club got off to the worst possible start.
The Eagles are the only Premier League team yet to win a game and their total of 450 minutes without scoring is the longest goalless run recorded by any side at the start of a Premier League season.
"We didn't deserve a fairytale ending," said the 70-year-old, who was appointed on Tuesday following the sacking of Frank de Boer, who lasted only four league games and 77 days at the club.
"We didn't play well enough. After the goal you could see the nerves and the anxiety. The only comfort I could take is that we got better as the game went on. The players care and they hurt and you couldn't say they weren't trying.
"We have to get better and sometimes it's easier to get better physically and technically than it is mentally. We need mentally strong players because the criticism will add up.
"The change of management has not brought the magic-wand effect but I still believe in the long run these players will pick themselves up off the floor, where they've been knocked to. We've got players with big experience and personality to come back into the team.
"I believe the work can be done on the training field if you have the right characters and we have those characters. We'll keep chipping away at that and we have to hope the fans, who will be bitterly disappointed, stay with us."
Analysis - 'There's no life in that interview'
Former England defender Danny Mills on Final Score
We've heard it all before. Where's the enthusiasm to lift these players?
He's talking about needing characters and being mentally strong, saying he can change them mentally and tactically, but you need something, you need life. There's no life in that interview. You look at that as a player and think, 'I'm not inspired'.
He could easily lose four out of the next five the way they played today. What does the chairman Steve Parish do then?