Ms Truss walked on to the stage at the Conservative Party conference to their 1990s hit Moving On Up, which features vocalist Heather Small, ahead of delivering her keynote speech.
The dance anthem, which was released by the Manchester-based band in 1993, peaked at number two on the UK singles chart.
Pickering told the PA news agency: “They (the band) are livid. Heather’s boy James is a Labour councillor. Hopefully most people will know that they have pirated it off us.
“She won’t be around to use it again for very long. I would imagine.”
He added: “I am absolutely gutted by it because they are killing the live touring of bands and artists… I am Mancunian and getting from Manchester to London these days is harder than getting on to continental Europe.”
Pickering said the band had contacted their lawyers but been advised there was little that could be done.
He said: “The rest of the band have rung me: ‘For God sake, how can we stop it?’
I was just looking at the lyrics. It’s amazing. I hope she takes note. It’s about, ‘Go and pack your bags and get out’
“And we just rang the lawyers and they went, ‘You can’t actually stop it. We can send a letter to cease and desist but you can’t do it’.
“They can play what they like, which seems a bit weird to me.”
Ms Truss entered to the track’s famous chorus “Movin’ on up, nothin’ can stop me. Movin’ on up, you’re movin’ on out. Time to break free, nothing can stop me.”
The opening lyrics of the song read: “You’ve done me wrong, your time is up”, with the last line of the first verse saying: “Move right out of here, baby, go on pack your bags”.
Pickering added that Ms Truss should pay attention to the lyrics of the song.
He told PA: “I was just looking at the lyrics. It’s amazing. I hope she takes note. It’s about, ‘Go and pack your bags and get out’.”
The son of the group’s lead singer Heather Small, James Small-Edwards, was elected as a Labour councillor for Bayswater, west London, in May.
Following Ms Truss’s entrance, he tweeted: “An apt choice! This tired and out of touch Tory Government is indeed moving on out.”
Small has also previously shown her support for refugee charity Care 4 Calais’s #StopRwanda campaign.
Asked why he thought the song had been used, Pickering replied: “No-one said to them ‘Tony Blair and New Labour used that song all the time’ or ‘Heather’s son is a Labour councillor’ or ‘Mike is really vociferous on Twitter and social media about being an anti-Tory’.
“I don’t know why they have used it. They are so useless at everything. Who knows?”
Ms Truss personally selected Moving On Up for her walk-on music, according to her press secretary.
He said: “There was a range of options and she chose that one.”
The press secretary was unable to say whether the party had asked for permission, adding: “I don’t have detailed knowledge of how the licencing of this stuff works.”
When asked about Pickering’s criticism, the press secretary said: “I don’t know who he is.”
Boris Johnson previously used Friendly Fires’ track Blue Cassette as he walked out for the party conference last year.
The indie band later hit out at the then-prime minister, saying their “permission was not sought” to use the song and that they had asked their management to ensure it was not to be used again by the party.