Roy Hodgson admitted Crystal Palace remain in a relegation dogfight despite their uptick in form but suggested the dog is now slightly smaller after four unbeaten games.
Palace won their first three matches under Hodgson after he was reappointed in March following a run of 12 winless games under previous boss Patrick Vieira, and followed it up with a goalless draw at home to Everton on Saturday.
That has helped move them nine points clear of the bottom three and within touching distance of safety despite losing star forward Wilfried Zaha to injury.
Palace will still be without the 30-year-old, who has missed the last three games after being forced off with a groin problem during the win against Leicester, when they face Wolves at Molineux on Tuesday.
Hodgson was hopeful of Zaha returning to training this week but confirmed he will not be available for selection until Saturday’s game against West Ham at the earliest.
The side have fared well in his absence, scoring five in a rout of Leeds at Elland Road and two more in victory at bottom side Southampton to put the spectre of relegation seemingly behind them.
Yet Hodgson said his players would be making a mistake to believe the survival job he was brought in to do was complete, and thinks his side are still in a scrap.
“I think the size of the dog we’re fighting might have got slightly smaller,” he said. “It’s still a fight, there’s no doubt about that. The dog is nowhere near as small as we’d like it to be.
“I’m not going to go as far as talking about mathematically safe. I still think that any team on 37 points that sits back and thinks that’s our job done is making a huge mistake.
“I think it would be an incredible lack of ambition and professionalism and desire to have six games in front of you and decide that 37 points will see us through.
“I came here in the hope that I would leave the club in the Premier League. If it so happens that we are there on 37 points and goal difference, so be it. That is something that I don’t contemplate at the moment. I think in those six games we’re capable of taking more points and getting ourselves fighting even smaller dogs.”
Asked whether Zaha would walk back into the team when he is fit, he replied: “The diplomatic answer is (the front three of Jordan Ayew, Michael Olise and Odsonne Edouard played well against Everton). The honest answer is that when Wilf is fit, he will play.
“I still think one is always going to be dependent on one’s best players, on one’s match-winning player. But to become a really good team you need more than one.”
Palace can move above Chelsea into 11th place in the Premier League with victory at Molineux, something which seemed unthinkable when Hodgson was appointed on March 21.
Then, the gap to the free-spending Blues stood at 11 points with the team more worried about being overtaken by sides beneath them than looking up the table.
However, a win against Wolves would see Palace in with a realistic chance of breaking into the top half as the season enters its final weeks.
Hodgson was asked whether chasing down the teams above them could keep the players motivated with survival almost secure.
“We’ll find ways of keeping the players concentrated and motivated, but the best way to do that is to make sure the competition for places remains very, very high,” he said.
“That’s the best motivation and inspiration we have. We won’t do it by targeting a team above us in the table. I didn’t come to the club really to try and make certain that after 10 games we finish above Chelsea. I shall definitely keep my feet on the ground and you won’t hear me talking about let’s catch Chelsea up.
“If we did catch them up after the gap that was there when I first came to the club then you should be talking more about what Chelsea are doing wrong than what we’re doing right, because Chelsea should not be caught by us with the big lead they had over us a month ago.
“With the amount of money and riches that they possess, I don’t think they should be looking at fearing that we should be overtaking them, a Crystal Palace team that has actually been fighting relegation for a period of time.”