Rams led 17-16 when Michael Knowles landed a drop goal with three minutes left, but a try by Gavin Bennion and Rob Fairclough’s conversion snatched away the points.
It was a savage blow for Rams who had also seen a 16-10 lead disappear through Bennion’s first try two minutes before the drop goal.
They remain fourth bottom in the Betfred Championship, but are just three points above second-bottom Swinton.
“It was similar to some of our early-season defeats,” Greenwood admitted.
“We had it won twice, but just crumbled in the last minute.
“It is hard to take – so hard to take, but there’s nothing else you can do other than just keep working hard behind the scenes and hope your luck changes and the learning improves.”
Greenwood is confident the late collapses which have been a feature of Rams’ season can be prevented, but added: “Whether the people in there now can improve or personnel have to change is my job to work out.
“It has happened too many times now for it to be a coincidence.
“We have been in a good position and have managed to lose the game.
“We have got to work out what needs doing to stop it happening again.”
Wins in those games would have left Dewsbury in a secure mid-table position.
“Even 50 per cent of them would be nice, we would be in a lot different situation, but we have lost them or given a point away,” Greenwood said.
“We are not in a good situation, but to be honest Swinton was the first one I felt we should be winning.
“Sheffield, York and Toronto are all in a better spot than us and it would have been a surprise [if Rams had won].
“We have pulled off two surprises – at Widnes and Featherstone – and the Barrow one [away draw] I am not sure about, but Swinton was the first one I went in confident, thinking if we both play at our best we are better.
“In the others I’ve always prepared my team to win and been confident we could win, but we’ve been underdogs.”