The Scottish Labour leader has been in London this week for talks with Sir Keir Starmer.
He warned senior party figures that Scotland was the first “red wall” to fall for Labour.
Mr Sarwar, who presided over a drop in seats for the party at May’s Holyrood election just eight weeks after taking on the role, said Scotland would be essential if Labour is ever to return to government at Westminster.
Speaking to the Daily Record on Thursday, Mr Sarwar said: “I’ve said directly to Labour MPs and to the shadow cabinet that the first red wall to fall was in Scotland, not the north of England.
“Unless they recognise that, until we get Labour back on the pitch again in Scotland, credible again, there is no route back to a UK Labour government.
“Now, it is on me to fix the Scottish Labour Party, but what also helps is a UK Labour Party that people believe will win a general election. They have work to do to get Labour into a position to do that.
“My message to the party, and to the country, is don’t repeat the mistakes that were made by Scottish Labour over the last number of years.
“Labour across the UK cannot win by creating our own version of ‘us versus them’ that turns half the country against the other half, like the SNP and the Tories have done.”
When asked how the party reverses its electoral fortunes in the UK, Mr Sarwar said: “The muscular unionism of Boris Johnson and the blindfolded nationalism of the SNP do not work.
“We have got to build a credible alternative to the SNP and the Tories. It has to be a positive, outward-looking, unified and authentic message to voters.
“The SNP and Nicola Sturgeon would love people to think England is Johnson and [home secretary] Priti Patel. England is more Gareth Southgate and Raheem Sterling – diverse, outward-looking, not scared of confronting the scars in our society.
“One of the big challenges for Labour is framing what Britain is. It is not inward-looking, angry, culture-wars Britain.”