The Romanian family living in the Conway House flat in Samuel Street were able to put out the fire.
But the attack is just one in a string of attacks from young people in the area.
Landlord Norbert Mazik, who owns a couple of flats in the building at Conway House, said: “They put a firework rocket through the letter box and they set the flat on fire.
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“Luckily the tenants managed to put the fire out.
“The police didn’t attend. We are talking about a block of flats - a four storey building.
“Crime is getting worse on the whole development but it feels like police don’t care about the situation.”
Before the firework was sent through the door the Romanian family, who have been living in the building for almost a year, had confronted the youths about windows they had smashed at the house.
But Norbert said: “They jumped on Ion, who is the father of the family, and beat him up and smashed more windows.
“My tenants say there’s no reason they are targeting them.
“They go to the shop and the youths are there and they shout ‘go back to Romania’. This kind of hate crime has been going on for a couple of weeks.”
A spokesman from Lancashire Police said: “We were called around 7.45pm on Wednesday, November 7 to an address on Samuel Street, Preston.
“It was reported a firework had been pushed through a letter box causing a small fire.
“The fire was quickly extinguished and no injuries reported.”