The shadow Brexit secretary said the country will remain divided regardless of the decision made after his party's proposed second referendum.
The claim came on the same day his party released its General Election manifesto with a promise to negotiate a new deal with the EU and hold a second referendum on the issue within six months.
Sir Keir said the only way to unite the country will be to take action to ensure people no longer feel disenfranchised.
He told a meeting in support of Edinburgh Labour candidate Ian Murray: "Anybody who thinks that the deal with Europe is going to resolve the issue, needs to think again.
"This isn't going to be resolved. There isn't going to be a happy day, when it's either the deal or remain is decided and it just goes back to normal.
"That's never going to happen."
Sir Keir, who was speaking alongside former prime minister Gordon Brown on Thursday, echoed an analogy made by a journalist in recent weeks, who likened Brexit to being pregnant.
He said: "It's like childbirth.
"'As soon as childbirth is out of the way, I'll go back to the theatre and spending time with my friends'.
"This is never going back and it's never going back because of the strength of feeling that came out of that vote in 2016.
"Because that phrase, 'Take Back Control', was a Heineken phrase. It really got into people.
"The more people were asked if they want the status quo, the more they answered no."
Sir Keir continued, saying the people who feel disenfranchised should be listened to and actions taken to change their views.
He also said it was important to give the people of the UK another vote on the issue.
He said: "If millions of people tell you that a political or economic situation isn't working for them, you've got to listen to that.
"We're never going to get past Brexit if we only focus on one part of it: the deal.
"We've got to focus on the other bit, which told us that we need much greater change than we've had for a long time.
"That told us that people feel disenfranchised at almost every level.
"The workers, in their health service, in their ability to believe they could trust their politicians and that has got to change.
"This will never be resolved if we don't match the deal that we come up with with a completely different offer for our country."