The train operator said it had been touch and go over whether the Pendolino tilting train would beat the 3 hours 52 minutes 40 seconds fastest time right up until it approached Glasgow Central Station.
Officials said the non-stop express had just missed overtaking the record time set 37 years ago by adhering to speed limits.
It reached platform one at Glasgow Central in 3 hours, 53 minutes and 1 second after travelling between England and Scotland’s largest cities at an average speed of 103mph.
Avanti tweeted: "In the words of So Solid Crew, we missed it by 21 seconds."
By contrast, British Rail’s Advanced Passenger Train (APT) reached more than 160mph on parts of its winning run in 1984 compared to the then speed limit of 110mph.
The Pendolino – named Royal Scot for the occasion in honour of the fastest service on the line in the heyday of steam – was limited to 125mph.
Avanti said both the train and track also had safety systems that limited speed, which did not exist in the APT’s era.
Its train was also slowed by a long-term 50mph speed restriction at Carstairs in South Lanarkshire, which is due to be lifted next year.
The attempt may have not been helped either by Network Rail chairman Sir Peter Hendy describing it on BBC Radio 4’s Today programme as involving a “bog standard” train compared to the APT, which he said had been an “experimental train that never really entered service”.
Rail expert Mark Smith, who was on board, said the Carstairs restriction "cost us 90 seconds".
He said: "It was a known risk but they thought we could still do it.
But it's still the fastest train I've ever taken from London to Scotland."
Avanti operations director Nick Westcott told The Scotsman: “We need to have another crack at the record next summer.
"We will have a bash before HS2 takes the wind out of our sails.
"We have one more chance to have another go before the whole profile of rail changes with HS2.
"As we came through Eglinton Street junction [on the approach to Glasgow Central], it was tight.
“By the time we reached Bridge Street junction [just south of the River Clyde], we knew there was going to be just seconds in it.
"But completing the 401-mile route with just 21 seconds in it wasn’t bad.
"It smarts a bit, but it has been good fun.”
Driver Neil Barker agreed – telling the PA news agency: "We'll just have to come back and try again."
The HS2 line between London and northern England is due to reduce London-Glasgow/Edinburgh journey times to 3 hours 37 minutes, with HS2 trains continuing north on the current west coast main line.
Avanti said no disruption had been caused to other trains by the record attempt and it praised track owner Network Rail for minimising speed restrictions.
Its normal London-Glasgow services take around 5 hours.