But he said he was "not worried" about scaremongering accusations.
And he predicted Labour leader Jeremy Corbyn - criticised for not taking a more prominent role so far - would be involved in "major events" to come.
Anti-EU minister Chris Grayling, meanwhile, criticised "over-the-top claims" about the dangers of leaving.
In a speech in Brussels, the House of Commons leader dismissed claims the UK could no longer trade with the EU if it left.
"Millions of jobs around the EU depend on selling goods and products to UK consumers," he said.
Voters go to the polls on June 23 to decide whether the UK will remain a member of the EU.
EU exit supporters have labelled the Remain campaign "project fear" after repeated warnings over jobs and investment.
But Mr Johnson, in an interview with The House magazine, said: "The fact is that if you're asking British people to wrench themselves away from Europe after 41 years, you're entitled just to point out the risks and dangers."
The former home secretary said he was confident of his side's arguments but added: "Whether we can row back against a deluge of anti-European nonsense that's come day after day, that's what worries me.
"We can't find the simple phrases. I have faith in the British people that they're going to be looking for more than soundbites and a bit of patriotic posturing."
He also said former prime minister Gordon Brown would make a "major intervention" in the EU debate, and on Mr Corbyn's role, added: "We don't want to fire all of our ammunition too early in this."
Labour's pro-EU campaign leader Alan Johnson says he worries his side does not have "simple phrases" to counter "soundbites" from opponents.