In a match reduced to 17 overs per side at Old Trafford, only seven were possible with Lancashire on 39-0.
But Warwickshire's win at Yorkshire and Worcestershire's victory over Notts saw the 2014 champions finish fifth in the North Group with a worse net run-rate.
Lancashire remain bottom of the group with just two wins.
Following a delay of more than four hours, play eventually got under way at 18:15 BST with each innings reduced to 24 overs, and Lancashire's Karl Brown raced to 30 not out.
The players went off for rain 30 minutes later, but it was hoped they could start again at 19:45 BST, with the match now 17 overs for each team.
However, the weather closed in again and they did not return - meaning both sides take one point.

At least 290 people were killed and hundreds more injured when the 6.2-magnitude quake struck in the early hours of Wednesday, 100km (65 miles) north-east of Rome.
The town of Amatrice was among the worst affected areas.
The service at St Andrew's Cathedral was led by the Archbishop of Glasgow, Philip Tartaglia.
It follows a similar event in Edinburgh on Sunday.
Ronnie Convery, director of communications for the Archdiocese of Glasgow, said there had been wide interest in the service from Scotland's Italian community.
"We are looking at something like 400 new arrivals from Italy every month at the moment in Glasgow and Edinburgh," he said.
"It's those people I notice on social media who have really taken up the information about the mass today.
"It's also interesting that in many cases people are not necessarily practicing Catholics but they just want to have that opportunity to be together, to meet, to do something."

A spokesperson said it had taken the move because the post violates Facebook's community standards.
It comes after a series of paramilitary-style attacks in the Turf Lodge area.
The PSNI said they were not linking the post to recent shootings at this stage.
Police said such paramilitary style attacks in west Belfast had doubled in 2016 compared to 2015.
The police figures do not take into account the Turf Lodge shootings.
Speaking on the BBC's Good Morning Ulster programme, before the post was removed, Sinn Féin MLA, Pat Sheehan, said that some people on the list had already been shot.
Mr Sheehan said the name of the 26-year-old, who was shot in both legs on Tuesday night, was on the list.
"My understanding is that this man's name has appeared on a list on social media, a list that contains eight names and photographs of people," he said.
Mr Sheehan added that the list accuses people of so-called joy riding.
There have been a number of shootings since the beginning of the year.
Mr Sheehan said: "A number of people on this list have already been shot and it's my understanding that police have begun to visit others whose names are on this list to warn them about their security.
He said the community did not believe there was a drugs link to the attacks.
"The people who have been shot, and I exclude the couple from last week, mostly have been involved in anti-social behaviour and petty crime.
"It's a well-known fact that these people who are carrying out the shootings actually tax drug dealers and if these people pay up their tax, they aren't being shot.
"The community is having to deal with the fall-out of all of this," he added.
West Belfast People Before Profit MLA, Gerry Carroll, said he was "deeply concerned" that an "apparent hit list" of people had been published on social media, with three of those on the list being the victims of recent punishment shootings.
"So-called punishment shootings are inherently undemocratic, inhumane and wrong," he said.
"Nobody in west Belfast selected the individuals who compiled this list as their judge, jury and executioner. This is a community that understands the effects of repression and injustice.
"People don't want an even more repressive 'punishment' system foisted upon them without their say."
Durham were eliminated from the One-Day Cup after their match against Lancashire was abandoned and other results went against them.
[NEXT_CONCEPT]
A mass has been held in Glasgow to remember the victims of last week's earthquake in central Italy.
[NEXT_CONCEPT]
Facebook has confirmed that it has removed a post on its site which included names and photographs of people accused of anti-social behaviour in west Belfast.