It marked the first time Tories have been elected in Sandwell for nearly a decade, and came after a chaotic run-up to the elections which saw a number of senior councillors quit the Labour party, including former leader Yvonne Davies.
Councillor Crompton, who held onto her Tividale seat by just 150 votes, said infighting among members of the Labour group had put people off from voting for party candidates.
She continued: “Personally, I think we need to have some deep conversations.
“I have been saying that the Labour Party need to work together, for many years now. I have not changed my mind. I have always been the voice of reason.”
Labour officials believe the huge Tory vote in the Black Country – the party made more than 30 gains across the four boroughs – was partly down to the success of the vaccine roll-out.
However, Labour councillors in Sandwell, as well as the borough’s only remaining Labour MP John Spellar, believe the party will come back stronger.
Councillor Crompton said: “I think Labour will bounce back.
“At this point in time, I am not certain how that will work. But people will be having huge conversations to see which is the best way to go.
“And personally, we need to listen to what the people are saying.”
It is not yet known whether Councillor Crompton will continue as leader, or whether an internal election will be held which would see a fifth leader for the council in two years.
Langley councillor Mrs Davies, who was suspended by Labour last year over social media posts, was another to quit. She accued her old party of trying to "bury the truth" and claimed Labour now "lacked all moral authority".
Cabinet member Councillor Joanne Hadley was another to go, saying her decision was down to “ongoing attempts to cover up political corruption in the Sandwell Labour Group”.
The controversy has dragged on since the publication of the Wragge report in 2016, which contained allegations of corruption against elected members.
Since then there have been numerous claims of interference in local matters by the national party, with former West Bromwich West MP Adrian Bailey claiming Labour's National Executive Committee had made decisions that were "hugely damaging" for the party on a local level.
Sir Keir Starmer addressed the chaos in Sandwell in the weeks before the elections, insisting his party was "making changes" that would benefit the borough's Labour group.
Warley MP Mr Spellar conceded it was "not a good year" for the Labour Party but insisted the party would bounce back.