"Scottish Labour is now the party of change and tonight demonstrates Scotland will lead the way in delivering a Labour Government."
Following the loss, Yousaf described the evening as a "disappointing" for his party.
The First Minister said: "We lost this seat in 2017, and like 2019 we can win this seat back. However, we will reflect on what we have to do to regain the trust of the people of Rutherglen and Hamilton West.
Turnout for the vote was 37.19 per cent, a huge fall from the 66.5 per cent recorded at the last general election.
Michael Shanks, won over 17,000 votes, out of a total of 30,000 cast - more than double the number by SNP's Katy Loudon
The by-election was called after a recall petition against Margaret Ferrier, who had won the seat for the SNP in 2019.
However, Ferrier had the SNP whip removed after breaching Covid rules in 2020.
She remained as an independent MP but was suspended from the House of Commons, resulting in the recall petition.