New Zealand First leader Winston Peters also said he was not consulted.
Mrs Turei rejected Mr Little's description of her as inexperienced, saying she had been co-leader of her party "for five years, not five minutes".
She said the mistake could be down to Mr Little being new to the job, and the two parties would be able to repair their relationship if Labour was willing.
Mr Little said he stood by his decision to nominate Mr Shearer to join Mr Little on the committee, saying he needed someone with the relevant skills and experience and had not wanted to upset NZ First by giving it to the Green Party.
Prior to the election, Labour had given one of the two Opposition places on the committee to Dr Norman.
Mr Little said Dr Norman's decision to step down as leader and scale back his political involvement was a factor in his decision. Potential future coalition arrangements also had a part: "The risk is, of course, as we're trying to build the coalition, if I chose somebody from the Greens, NZ First might be affronted. If I chose somebody from NZ First the Greens might be affronted too."
He said he stood by his decision, but admitted he could have told the Green Party of it in advance rather than letting the party find out from the media.
He said Labour enjoyed "good cordial relations" with the Greens and that would continue. When told that was not the Greens' view this morning, Mr Little suggested "ask them again tomorrow morning".
Dr Norman tweeted his outrage this morning, accusing "LabNat" of cutting the Greens out.
"Old boys' club regains control of (weak) parliamentary committee of oversight of Government spies."
He also said Ms Turei would have been the one on the committee rather than himself, given his decision to step back.
The committee will be involved in a major review of the intelligence agencies this year. That review was set up in law changes to clarify and expand the GCSB spy agency's powers, as well as lift oversight of the agency after it was found to have potentially illegally spied on about 180 New Zealanders outside its powers.
Dr Norman said there were abuses of power under both Labour and National governments: "Illegal spying at GCSB happened under Lab and Nat ministers. And SIS persecution of Zaoui happened under Lab -- courts found SIS in wrong."
However, Prime Minister John Key welcomed Mr Little's choice of Mr Shearer, saying the Green Party had used their position to turn the committee into "a political battle ground".
He said it was important the committee worked in a bipartisan way if possible, and it had not been "terribly constructive" in recent years.
"I think it was used less as a way of constructing the right outcomes for legislation and more as a sort of political battleground."
Mr Key planned to nominate himself, New Zealand Security Intelligence Minister Chris Finlayson and Justice Minister Amy Adams for the committee.
Mr Little said he had not discussed the matter with Mr Key "but I'm happy to have his blessing".
Mr Shearer said he had been on the committee in the past when he was Labour leader so knew how it worked.
In his time as Labour leader, Mr Shearer had allowed Dr Norman to hold the second slot but he said it was Mr Little's call.
"It was an offer to me, and I accepted it. I don't think it should make a difference [to the relationship between Labour and the Greens], but I think, again, it is what Andrew believes is the right thing to do."
