Baroness Morgan said Labour is in a serious situation if it cannot reconnect with working class communities.
She said there "probably was an element" of Labour's Remain campaign starting too late.
"A lot of us were exhausted", she told BBC Radio Wales.
Senior Welsh Labour sources have privately said they were wary of talking about Brexit before the assembly election in case it drove Eurosceptic supporters towards UKIP.
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Asked if Labour's Remain campaign started too late, she told the Eye on Wales programme: "I think there probably was an element of that.
"And don't forget in Wales we had the assembly elections where people were not talking about the European Union. We were focused absolutely on those assembly elections."
She added: "I think it was a mistake not to be talking about the European referendum in those assembly elections."
Wales voted 52.5% to 47.5% for Brexit. Only five counting areas voted to Remain.
The strongest Leave votes were in Torfaen (60%) and Blaenau Gwent (62%) - two traditional Labour strongholds in the south Wales valleys.
The Welsh government has a programme to "re-energise" communities that voted to Leave, much of which would have been funded by EU money, Baroness Morgan said.
"The question for us now is how on Earth do we reorganise the economy without that European funding?" she asked.
"Unless we find a way to reconnect with that working class element within our communities then I think the Labour party is in a serious situation in future".
Labour won 29 seats at May's assembly election - a better result than many expected - but lost 7.6% of its share of the vote on the constituency ballot.
Earlier, on BBC Sunday Politics Wales, Baroness Morgan said Carwyn Jones was "absolutely, without question" the right man to lead Welsh Labour.

The Glasgow Warriors wing was initially left out of the squad for the two-Test trip, but injury to Tim Visser resulted in a call-up for the 35-year-old.
Lamont made his Scotland debut in 2004 and turned out for the 104th time during this year's Six Nations.
"When I was left out I was absolutely gutted. To get the phone call again was very nice," he told BBC Scotland.
"I love playing for Scotland it's a massive part of what I've grown up doing for 12 years now.
"It's been a big part of my life and I sure as damn don't want it to go away."
Lamont may be close to Paterson's record but realises that with every passing Test the competition for places in Vern Cotter's line-up is greater, with younger players breaking through.
"Eventually it will have to finish but it's been a fairly emotional roller coaster," he explained. "The disappointment of not getting the call-up and then getting the call, so it's nice to still be on that list.
"If someone's ahead of me I like pushing myself to get ahead of them, that's the way it should be.
"But in the cold light of day it's down to the coaches to make the choice.
"I know where I am in my career, I'm all for pushing the next generation through - it's good for Scottish rugby, it's something we need, so the more competition it's good for the player and the country."
The Scots are unbeaten in five meetings with Japan, with the last encounter a 45-10 victory at the World Cup in 2015.
Japan are 10th in the world rankings, one place below Scotland, and Lamont expects two strongly contested encounters in Toyota City and Tokyo.
"They're going to be two tough Tests, no shadow of doubt," he said.
"They'll be geed up because of the run they had at the World Cup, they'll be looking to claim a scalp and boost the profile of Japanese rugby.
"Things like home advantage and weather, I think it'll be hot and humid over there, and above all they're a good team so we've got be very wary.
"They pushed us in the World Cup for a good 60 minutes, but towards the end we ran away with it, but it was by no means easy, there were some real sticky moments."
BBC Scotland will provide live television, online and radio coverage of the Tests on 18 and 25 June.
It was a mistake for Labour to avoid talking about the EU referendum during the assembly election campaign, one of the party's AMs has said.
[NEXT_CONCEPT]
Sean Lamont aims to take a step closer to Chris Paterson's Scotland cap record of 109 on the summer tour of Japan.