The prime minster told ITV News Political Correspondent Paul Brand that "solutions can be found for frictionless trade with Northern Ireland" and suggested technological ways around the backstop.
When asked explicitly whether he believed Theresa May didn't make the case for backstop solutions convincingly enough, Mr Johnson said "yes, absolutely".
He said: "What I am saying is that if you look at what the UK government was doing, it was basically reconciled psychologically, emotionally, intellectually to remaining within in the Customs Union and orbit of EU law."
He added: "None (of the solutions) have been properly suggested by the UK and I think it's very important that we cannot agree to a Withdrawal Agreement - the current Withdrawal Agreement - that I have said many times is a dead letter."
Mr Johnson also said Donald Tusk's rejection of his request for the backstop to be removed from the Withdrawal Agreement was "curious".
He said: "I think it's a bit paradoxical that the EU side is talking about us putting up all the barriers, we've made it clear 1000 times we don't want to see any checks on the Northern Irish frontier at all."
Mr Johnson had written to Mr Tusk, setting out his vision to remove the backstop from the Withdrawal Agreement and break the Brexit deadlock.
ITV News Political Correspondent Paul Brand explains the Prime Minister's fresh ideas - or lack of
In Mr Johnson's letter, he said while he wants the UK to leave the EU with a deal, he could not support any withdrawal agreement that "locks the UK, potentially indefinitely, into an international treaty which will bind us into a customs union and which applies large areas of single market legislation in Northern Ireland".
Mr Tusk responded on Twitter, writing: "The backstop is an insurance to avoid a hard border on the island of Ireland unless and until an alternative is found.
"Those against the backstop and not proposing realistic alternatives in fact support reestablishing a border. Even if they do not admit it."
Responding, Mr Johnson said: "We think there is a big opportunity now for everybody to come together, take out that backstop."
He added: "We will be looking at all the ways in which we can maintain frictionless trade at the Northern Irish border - whether it's trusted trader schemes, or electronic pre-clearing, or whatever it happens to be, all that kind of thing, checks away from the border, points of sale or whatever if you have to crack down on smuggling, all that kind of thing - but we will come up with those solutions, or agree those solutions I should say, in the context of the free-trade agreement.
"That's the way we are going to approach it. And you know what, at the moment it is absolutely true that our friends and partners are a bit negative.
"I saw what Donald Tusk had to say and it wasn't relevant of a sense of optimism. But I think actually we will get there."
Mr Johnson's comments come ahead of meetings with German Chancellor Angela Merkel on Wednesday and France's Emmanuel Macron on Thursday.
On those meetings, he said: "I'm going to go of course and see if I can explore those ideas with our friends in Germany and France and at the G7 - let's see where we get to. It may be that for now, they stick with the mantra."
He added: "(They say they) can't change a jot or a tittle of the Withdrawal Agreement...let's see how long they stick to that, I think there are plenty of other creative solutions."
Johnson 'misleading' people around Brexit situation, Brussels says
Officials in Brussels have privately accused Mr Johnson of making "incorrect" and "misleading" claims about the situation.
In public comments, the European Commission said the Prime Minister had failed to put forward a "legal, operational solution" to the issue and had acknowledged that if one could be found it might not be ready in time.
European Commission spokeswoman Natasha Bertaud said the letter "does not provide a legal, operational solution to prevent the return of a hard border on the island of Ireland.
"It does not set out what any alternative arrangements could be and in fact it recognises that there is no guarantee that such arrangements will be in place by the end of the transitional period," she said.
An official briefing note circulated among diplomats from the member states made clear the EU's frustration with Mr Johnson's approach.
The document, seen by the PA news agency, disputes Mr Johnson's claims about the Good Friday Agreement and the Irish border.
It was "incorrect to state that the people of Northern Ireland have no influence over the legislation that would apply to them" and "misleading" to suggest that the two separate jurisdictions that exist on the island can be managed with an open border because that was only possible now due to the framework provided by EU law.
Any attempt to remove the "vital insurance policy" of the backstop would also be rejected by MEPs, the European Parliament's Brexit co-ordinator Guy Verhofstadt indicated.
"The time for bluster & political blame games is fast running out," he added.