A court heard on Monday that Mr Dallas and his family were watching highlights of an Old Firm game - during which the referee was struck on the head with a coin - when a bottle smashed two windows.
Self-employed joiner Kevin Dunn was found guilty of throwing the bottle at the house, despite his assertions that he was nowhere near the property.
The incident happened after the controversial Old Firm clash in May 1999 when Mr Dallas sent off Celtic players Stephan Mahe and Vidar Riseth and Rod Wallace of Rangers.
Windows were smashed at the Dallas home
The referee required four stitches in a head wound after being struck by a coin during the match and four fans attempted to attack him on the pitch.
The 3-0 victory secured the league title for Rangers.
North Lanarkshire District Court in Motherwell heard that Mr Dallas was recovering at his £200,000 house in Carfin, Lanarkshire, after the Parkhead match.
He was watching highlights with his wife Jacqueline, their son Andrew and his girlfriend Kerry McFadyen at about 2300 BST when there were two loud bangs.
As Mr Dallas and his son rushed to the front door they saw Dunn strolling out of their driveway with a blank look on his face.
'Opened the door'
He told depute fiscal Stephen McGowan: "We could see someone passing. He was right in front of the door.
"By the time I opened the door he was passing between two cars in the driveway."
When asked if he knew who the person was, he replied: "Yes, it was Kevin Dunn."
Mr Dallas said he had known Dunn - who lives close to the referee's home on the Dalzell Estate - socially for about 20 years.
He said: "My son decided to run after him. I said not to bother because we would let the police deal with it."
My mum was frightened, so was my girlfriend. We were worried about the two females
Two double-glazed lounge windows had been smashed and a beer bottle was lying among shattered glass. The damage cost between £200 and £300 to repair.
Andrew Dallas, now 17, said Dunn had "a glazed look on his face".
He added: "My mum was frightened, so was my girlfriend. We were worried about the two females."
Dunn went to Motherwell Police Station the next day and denied any involvement in the incident.
'Not deliriously happy'
He said he had been at the match with a neighbour, his nine-year-old son Barry and the neighbour's daughter.
He said he had been at the Dalzell Country Club for a couple of drinks, but was nowhere near the Dallas house.
He said: "It wasn't me. I wasn't there."
Dunn was not "deliriously happy" with the result of the game, but could not say whether or not Mr Dallas' decisions were controversial.
He added: "It was a Celtic/Rangers game with the usual atmosphere.
"My boy was there and I'm not the sort of person to get caught up in the atmosphere.
"When I saw the blood coming down Mr Dallas' face, I felt sorry for him."
Sentence was deferred on Dunn for a year after he was found guilty of smashing the two windows.
Chairman of the Bench, Edith Ryan, JP, told him he would be admonished if he was of good behaviour.