Extra restrictions were imposed after Covid-19 infections rose in the city.
Adrian Phillips, chief executive of Preston City Council, said it was "alarming to see that the under-30s are contracting it at a significant rate".
"I know our director of public health has said 'Don't kill Granny' to young people to try and focus the message,'" he said.
Since midnight, residents in the Lancashire city are banned from mixing with people from outside their social bubble in homes, gardens, and indoor venues, such as pubs.
They can meet in groups of up to six - or more than six if they are from two households - in outdoor areas such as parks and beer gardens.
he restrictions will be reviewed next week, with any changes due to be announced by Friday.
It comes after similar rules banning residents from visiting people's homes and gardens in Greater Manchester, East Lancashire and parts of West Yorkshire came into force on 31 July.
Socialising between people from different households in pubs and homes had been seen as the main cause for the spike, local authorities said.
Dr Sakthi Karunanithi, Lancashire's director of public health, told BBC Breakfast that "47% of positive cases are in younger people - 30 years and below".
"Contrary to the common myth that this affects the south Asian groups the most, we have found that it's roughly affecting white ethnic backgrounds as well as south Asian groups in Preston almost equally," he said.
Local officials said the spike was particularly among those living in poor socio-economic conditions, including inner city and rural areas.
There were 61 new cases in Preston in the seven days to 4 August. This is the equivalent of 42.6 cases per 100,000 people - up from 21.7 per 100,000 in the previous seven days.
Mr Phillips said younger people "often have less symptoms but they do take it back to their household".
He said local authorities were working with community groups who were doing "peer-to-peer communications".
"It's just trying so many different ways to get the message to all communities, to all areas of our city that the virus is still something to be really wary of," he added.
Nadeem Ashfaq, from inter-faith group the Light Foundation, said parts of the city had been "really quiet" overnight and on Saturday morning.
"Everywhere I have been, I see people with masks," he said.
The announcement of new lockdown restrictions had not been a shock, he said, as people had been made aware of the city's rising infection rate in recent weeks by local authorities.
"If you look at other towns and places, you can sense there was an upheaval. I think in Preston there seems to be a calm understanding," he added.
Hannah Heaton, 28, said she thought the new restrictions were confusing.
"It doesn't make sense that you can't go to houses but you can meet people outside or go to pubs," she said.
"My grandparents rely on me to help them and now going to see them has been taken away from me.
"There's nothing I can do about it. I think certain people haven't been taking it seriously because they don't think it will affect them."
Charlene Gardner, 38, said: "The pubs around us were still 30 or 40-deep outside last night.
"It won't mean any changes for us because we haven't been seeing family anyway, but I saw some reaction online last night and I think a lot of people aren't going to listen to it."
Many people in the main Fishergate shopping street were wearing masks, and a face mask seller, who did not want to be named, said the city was less busy than the previous weekend.
"You see the older people wearing masks but the younger ones don't. The problem is in the pubs and they don't wear masks there," he said.