Manager Roy Hodgson said there would be no quick fix at Crystal Palace, after his side beat Huddersfield Town 1-0 in the third round of the Carabao Cup.
Bakary Sako headed the only goal to give Hodgson the first win of his tenure, in his second match in charge.
However, Palace remain without a win or a goal from five Premier League games.
“The players will understand, like the fans do, that you don’t repair the kind of damage we’ve suffered overnight,” said former England manager Hodgson.
“It’s going to be a longish and hard process. But I know there’s light at the end of the tunnel, and I started to see some shards of that.”
Palace were on the back foot for a lot of the second half but held firm thanks largely to centre-back Mamadou Sakho, making his first start since joining the club on a permanent basis.
The victory signifies progression from the Eagles, who were beaten 3-0 by the same opponents on the opening day of the season.
“The week’s work has really pleased me,” said Hodgson. “I’m pleased with the win, pleased with the first-half performance after only a week’s work.
“The second half I was pleased when the going got tougher; we had to dig in, fight, chase and we did that too. It was a very positive evening. We left a lot of players out who have been playing.”
Palace lost their first game under Hodgson 1-0 to Southampton. They travel to both Manchester clubs next, before playing Chelsea at home.
Defender Pape Souare came on as a substitute against Huddersfield to make his first appearance for the Eagles since breaking his thighbone and jaw in a horrific car crash last September.
“He made two very important challenges,” said Hodgson. “Once again, I’m delighted with him.
“We’ve got to be cautious and patient with him. You don’t have a year out of football with the injuries he’s had to recover from, he’s done ever so well to get on that field at all.
“We just have to keep training him, getting him some more games, so he comes back to the player he was before the horrific accident.”