Palace had twice as much of the ball and three times as many shots on the opening weekend of the season but, helped by two goals being correctly disallowed for offside, the Blades were able to restrict the margin of defeat to 1-0.

If that sounds defeatist, it was a reflection of a teamsheet which showed a team significantly weakened from the one which won promotion from the Championship last season.

Iliman Ndiaye and Sander Berge have been sold, James McAtee and Tommy Doyle have returned to Manchester City after loans and even Oli McBurnie was injured. Gustavo Hamer was signed too late from Coventry City to replace Berge and Benie Traore was only the new signing in the starting XI, the rest coming off the bench.

Asked if it was a case of his players working hard but not being good enough, Heckingbottom replied: "You summed it up. That's what I said to the players. I can't be critical.

"I think we needed the first goal as well, if I'm honest.

"We were compromised with the way we want to play with the difference in the team but I felt we still by being disruptive, by being aggressive, had an impact on the game, especially first half.

"To concede the first goal early in the second half made the game more difficult, they've got the experience, they managed the game well and they've got top talent at the top end of the pitch that means they're a threat on the counter. It made it difficult."

He took heart from the fact that despite a strong performance by goalscorer Odsonne Edoaurd, well supported by the likes of Eberechi Eze, the Blades were a moment of good luck or of brilliance from equalising right until the end – even if neither never really looked like happening.

"I don't think there's anything there (to be afraid of) and I'm not being disrespectful to Palace because they're a well-established team with top experience on the pitch and certainly in the dug-out and they've got some real quality as well.

"I've not come away from there scared, the players shouldn't come away from there scared, because everything we should do from this point we should start improving."

With a game at Nottingham Forest on Friday and a visit from Manchester City before the transfer window closes on September 1, it is essential Heckingbottom is able to add greater quality so his squad can have a fighting chance of beating the odds and avoiding relegation.

"We've already signed a couple of players, Vini (Souza) came on for 25 minutes, Gus (Hamer) is in the building," he said. "That's more a reflection of where we are, we need to start getting bodies in and we will do.

"We've sold players so we've got the money to spend, we want to spend it. There might be one or two go right to the end in terms of loans but there's certainly one or two I would love to have in before the next game."

Palace manager Roy Hodgson was complimentary about the Blades, saying: "What Paul and everyone at Sheffield United will take most heart from is the fact the team played with so much heart. They have such a lot of determination they managed to summon up energy sometimes some teams might not be able to summon up when they've had such a long period without the ball.

"They never stopped chasing long balls forward, we had to be on our guard and on our toes not to make a mistake."

Paul Heckingbottom 'cannot criticise' Sheffield United after they are caught short against Crystal Palace