The wreckage of the three-tonne Eurocopter has been removed from the Clutha, which was badly damaged following Friday's incident that has left nine people confirmed as dead.
Clutha regular Jim Sheridan, Labour MP for Paisley and Renfrewshire North, said he often solved the world's problems in the pub on a Saturday afternoon only to find them still there when he woke up the following morning.
Mr Sheridan said Glasgow needed a venue like the Clutha and called on the commercial sector to rebuild a new one from the ashes.
Mr Carmichael said he had heard warm words expressed about the pub, adding to Mr Sheridan: "Like you I would like to see it resurrected."
Mr Sheridan had told Mr Carmichael: "Glasgow needs a Clutha. So I would ask if you could work with the commercial sector to rebuild from the ashes a Clutha Vaults because Glasgow really needs it."
He also told MPs: "In recent years I've become a regular customer in the Clutha Vaults. In fact the Saturday afternoon just gone I had scheduled to meet some comrades in the Clutha Vaults, I say comrades deliberately because it was that kind of place.
"On many a Saturday afternoon I solved the world's problems in the Clutha only to wake up on the Sunday morning and they were still there.
"But just recently I met with some firefighters in the Clutha Vaults who were telling me about their concern about their jobs, terms and conditions and I would hazard a guess it's the same firefighters and other emergency workers who responded so quickly to what happened.
"The first victim that was led from the tragedy was a man from Paisley, Gary Arthur, and I'm sure (Shadow foreign secretary Douglas Alexander) will share with me and pass on our condolences to Gary's family."
On shadow international development secretary Jim Murphy assisting the rescue effort, Mr Sheridan said: "He doesn't frequent pubs very often and I'm very sure he would be the first to admit that the Clutha Vaults would not have been on his priority list to visit.
"But the important thing is that he could have driven by without anybody knowing where he was or what he had done.
"Instead of that he reacted and for me that's a measure of the man."