Mr Mason said the victory had sent a message to Downing Street.
Labour minister and Scottish MP Douglas Alexander said his party needed to "learn the lessons" from the "bad result".
He added: "We will continue to reflect on these results in the days and weeks ahead because actually we do hold ourselves to a high standard. We do want to serve not simply one part of the country but every part of the country.
GLASGOW EAST RESULT
22.54% swing from Lab to SNP
Turnout: 26,174 [41.2%]
"It hurts us to lose a seat like Glasgow East and we are determined to win it back."
Defeated Labour candidate Margaret Curran said she did not regret standing in the by-election, but added: "I regret that I did not win this for Labour tonight.
"I do believe the Labour Party has to listen and has to hear the message from the people of Glasgow East."
Mr Mason said: "Three weeks ago the SNP predicted a political earthquake.
"This SNP victory is not just a political earthquake, it is off the Richter scale.
"It is an epic win and the tremors will be felt all the way to Downing Street."
BBC Scotland's political editor, Brian Taylor, said it was an appalling result for Labour in a constituency it had held in various guises virtually since the party came into existence.
He said: "Will it add to the pressure on Gordon Brown? Of course. Frankly, though, I don't expect him to stand down any time soon.
"He already knew he faced a tough fight. It will, however, increase the trepidation around him."
Nine candidates stood in the by-election, sparked by the resignation of Labour's David Marshall on health grounds.
Margaret Curran speaks after losing the by-election
Scottish Tory leader Annabel Goldie, whose party leapfrogged the Liberal Democrats into third place, said the vote had "a powerful and positive message".
She said: "Labour is mired in failure. Throughout the UK it is the Conservatives who are setting the political agenda."
Scottish Lib Dem acting leader Michael Moore said his party's by-election candidate, Ian Robertson, fought a strong campaign.
"I am confident that Liberal Democrats will continue campaigns like the fight against the planned closure of Parkhead fire station long after the media circus has left town," said Mr Moore.
Scottish First Minister and SNP leader Alex Salmond said of the result: "I don't think we will see an immediate exit for Gordon Brown from Downing Street. I think it is more likely he will change policy rather than change himself."
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