Nigel Pearson admitted his frustration at failing to pull off their first back-to-back victories of the season although admitted they gave everything to pull off three points.
Bristol City were clinging on by the skin of their teeth in the opening 45 minutes as Sheffield United flexed their muscles in a dominant showing and perhaps felt fortunate to go in at half-time level.
Keeper Dan Bentley in particular would have breathed a huge sigh of relief on two occasions when he was caught wildly out of possession but he did make a great save to deny a header in the opening 10 minutes.
The hosts came out with plenty more attacking threat in the second period and took the lead through Chris Martin's 10th of the season when he finished from close range after some great work by Antoine Semenyo.
Arguably Sheffield United's best player on the pitch Morgan Gibbs-White would equalise 11 minutes later but the hosts had their chances to secure the victory with Semenyo and Nahki Wells guilty of missing good opportunities.
Manager Pearson was happy with the application shown by his side and admitted he can have no complaints with his players after following their determination to push for a winner.
He said: "I was pleased with the player's application today and their desire to try and win the game, we still haven't won back to back games which is a frustration.
"But when you get a performance like today for me that's not because we haven't tried to do it, the players are really committed to it and that's what we need to do more.
"We did create some very, very good chances. We tried to win the game and that was, I think you could see that neither side were interested in the draw, we were both trying to win it.
"The first half we struggled to get any rhythm with our own play, we probably gave the ball away too easily but I give them credit for it as well.
"They're pushing to or to cement their place in the playoffs so we knew it was going to be a tough game. I thought we played well."
Asked what Pearson said to his players at half-time, he responded: "It was just encouragement to try and get better possession from our defensive third through the third so that we weren't always asking our strikers to fight for the difficult balls and I think we played with a bit more control in the second half with a bit more tempo.
"Both halves were honest, I'm not going to be critical of the first half, we worked really hard and defended the goal really well and throughout the game, we had the best chances."
While Andi Weimann was forced to wait another game to grab his 20th of the season, Martin hit double figures for the second season in the previous five years - although Pearson feels he is deserving of more.
"He deserves more than that," he added. "He's worked hard this season and he's always been involved in our goals so whether he's had chances himself or created for other people.
"For a side in the position we are, to have a striker on 19 goals and another on 10, our season-long problem has been the number of goals conceded."
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