The shadow foreign secretary took aim at the perceived front-runners during an interview with ITV News.
Ms Thornberry, who faces an uphill battle to remain in the contest, said there was a "squeeze" to get on to the ballot paper due to Sir Keir and Ms Long-Bailey dominating on opposing wings of the party.
She told the broadcaster's Calling Peston podcast that she suspected others in the race had been planning their leadership bids before December's disastrous general election campaign started.
"The truth is that I had a standing start, so I threw everything into the general election and I started after the general election. I don't think that's necessarily the case with everybody else," she said.
"I started after the general election and we now have two machines, and we have two machine politicians, one on the left and one maybe perceived to be on the right. And there's a bit of squeeze going on."
Asked to confirm who she was referring to, Ms Thornberry replied: "Rebecca on the left and Keir on the right. "
Her comments come as shadow Brexit secretary Sir Keir announced he would be cancelling Labour leadership campaign events in the run-up to the weekend because his mother-in-law is critically ill in hospital.
He will not take part in the union hustings organised by Unite on Friday as a result of the pause.
Sir Keir and Wigan MP Lisa Nandy are the only two of the four remaining candidates to have made it through to the final stage, having each been backed by at least two unions and one socialist groups representing at least 5% of the total affiliated membership.
Shadow business secretary Ms Long-Bailey is widely expected to secure nomination from Unite, an endorsement that could pave the way for her to reach the ballot stage.
Islington South and Finsbury MP Ms Thornberry has yet to receive any union backing and is likely to need to secure nominations from 33 Constituency Labour Party (CLP) branches - equivalent to 5% of all CLPs - to ensure members and others can vote for her to be leader.
She currently has only three CLP nominations, meaning she must convince 30 more to back her before the February 14 deadline.
Despite facing difficulties in progressing, Ms Thornberry said she would not be following Jess Phillips's lead after the prominent backbencher threw in the towel and resigned from the contest this week.
The opposition frontbencher said she was "running to catch up" but would keep going because she was "popular" among the 500,000-strong membership who will decide the next leader on April 4.
A prominent member of outgoing leader Jeremy Corbyn's team, Ms Thornberry told the ITV podcast presenters she stood by the election manifesto's policies but criticised how they were presented to voters.
She said: "We were announcing four or five policies a day. This is not the way you do it."
The 59-year-old argued that Labour could have won an election if it had taken place following a second referendum, a position she lobbied for within the shadow cabinet.
"We should never have had a general election," she added.
"I argued really strongly that we shouldn't, I argued that we should have a referendum because a one issue election is a referendum and we should have got Brexit done by putting Boris Johnson's deal, or any other deal which is viable, to the public."
Asked if Labour could have won a majority under Mr Corbyn following another poll on Europe, she replied: "Of course."