A new report into the city's schools said that the progress made by white British pupils, especially boys and those from disadvantaged backgrounds, is poor compared to other children.
It said progress made by black and minority ethnic pupils and children who speak English as an additional language is far better than white British students at both key stage two and four level.
And it warned that attainment gaps are 'not closing fast enough' for disadvantaged pupils and is n'increasing' in some cases, including progress at key stage two and four.
Education bosses have stressed that improvements have been made across many subjects and attainment areas and that Sheffield is improving better than the other core cities - consisting of Birmingham, Bristol, Liverpool, Leeds, Manchester, Newcastle, Nottingham and Sheffield - it is measured against.
They vowed to conduct further analysis focussing on the key challenges faced in the city.
Pam Smith, the council's head of Primary and Targeted Intervention said: "Focus work is required to drive improvement particularly in phonics, reading and attainment and progress with certain vulnerable groups, particularly white British disadvantaged pupils, and more so boys."
She added that Sheffield is now at or above the national average for a number of attainment and progress measures across foundation levels, key stage one, two and four.
The report, which outlined attainment and performance outcomes from foundation stage to A-level in Sheffield’s schools and academies, was discussed by councillors at Sheffield Council's Children, Young People and Family Support Scrutiny and Policy Development Committee.
In reading and phonics, Sheffield is in the bottom 10 local authorities while the attainment by secondary school pupils in maths and English is below the national average.
The report highlighted that disadvantaged pupils are of concern and that this group 'perform poorly on a number of measures'.
It added that the progress eight scores - the progress made by pupils leaving primary schools and leaving secondary school - for white British pupils is 'negative and worsening' - but is still better than other core cities.
Stephen Betts, chief executive of Learn Sheffield, told the meeting that the progress made by this group of youngsters, particularly boys, was a national problem, and not something just specifically happening in Sheffield.
The report also highlighted improved areas. Key areas of success included the maintained improvements by foundation stage children, the above national average achievements of key stage one children in maths and the improved progress made across all subjects at key stage two level.
Mr Betts said: "Sheffield is broadly in line with what is happening nationally. The city is at or above nearly half of the measures used.
"That is a sharp contrast to what has been happening historically in Sheffield."
He added: "Partnership work is the single biggest driving force of these improvements.
"We should celebrate these improvements but certainly be looking for more."
The report added that the percentage of primary school judged good or outstanding by Ofsted had improved, but the number of secondary schools with those judgements had fallen.