The shadow foreign secretary rolled her eyes after the BBC political correspondent pointed out there was a “fair amount” of disagreement within the Labour Party over Brexit.
Ms Thornberry attacked the Prime Minister’s Chequers plan, insisting it would not work.
The Labour Party frontbencher was quizzed about the European Council summit, in which the Prime Minister said a Brexit deal could still be achieved.
Ms Thornberry said: “The problem is, as it has always been, is that the Conservative Party can’t agree amongst themselves about what it is they want to negotiate.
“Given that they can’t agree within themselves, they can’t negotiate with the rest of Europe. It has been this way for the last two years we have just been watching a big psychodrama and it seems to me we are no closer to the Tories deciding what they want.
“If her plan is so great if Chequers really works, why would she worry about a backstop. The backstop is basically an insurance policy in case Chequers doesn’t work.
“Nobody really in their heart of hearts believes Chequers is going to work, because it won’t work, that is why the Europeans need a backstop. That is why the Tories are all fighting about it. Do you see what I mean?”
The BBC’s political correspondent Jonathan Blake stepped in highlighting problems within the Labour Party over Brexit.
He said: “There is a fair amount of disagreement within the Labour Party about the best way forward on Brexit.
“Isn’t the Prime Minister doing what she needs to do and making concessions, this is a negotiation after all.
“She says she is looking for a deal in the national interest.”
After rolling her eyes at the BBC reporter’s jibe, Ms Thornberry said: “What is in the national interest is what we have been saying, which is that we need to be in a customs union, that is the baseline and then graft it on top of that we need a free trade agreement.
“That is what we should have been doing for the last two years and the Tories are incapable of negotiating that.
“That is the way forward, that is the way you look after the economy and jobs, that is what is important.”
Following the summit, the Prime Minister insisted that there was still time to secure a Brexit agreement with the European Union.
She said: “What I have had from leaders around the table over the last hours… since I arrived here in Brussels yesterday, is a very real sense that people want that deal to be done.
“And I think if you look at some of the comments that have been made, Chancellor Merkel said where there is a will there’s normally a way.
“Jean-Claude Juncker said let’s focus on the large areas of agreement and it will be done. So, there is a real sense. So, what we’re doing is working to ensure that we can do this deal within that reasonable timetable. I’m very aware of the legislative requirements we have in the House of Commons and the period of time that will take.”
Mrs May also made clear she would accept an extension to the transition period only to ensure there was no hard border in Ireland if it proved impossible to implement the future partnership by the end of 2020.
The question of the Irish border remains the major sticking point in Brexit negotiations. The EU’s proposed backstop has been branded unacceptable by Prime Minister Mrs May and the DUP, as it threatens to create a border down the Irish Sea.