David McLetchie, Tory leader north of the Border, and Sir Malcolm Rifkind, party president, were united in the belief that it would be "madness" to split.
Sir Malcolm, who failed to win back Edinburgh Pentlands from Labour, said: "We have to understand that we are a Scottish Conservative and Unionist Party and you cannot go around arguing the case for Scotland's future on one hand and saying you want a divorce from the rest of the UK on the other.
"The idea of a breakaway is a complete nonsense.
How the vote breaks down
And Mr McLetchie added that he and his colleagues were in the business of growing stronger north of the Border and helping to rebuild the party nationally.
"I have no desire to formulate a Tory policy on defence, foreign affairs, immigration and social affairs or the rest of it.
"We have got more than enough to do concentrating on the 2003 election for the Scottish Parliament where we will be fighting on health, education, transport, law and order," said
The rebuilding of the party north of the Border will now begin in earnest following the departure of its chairman Raymond Robertson.
He stepped down on Friday after failing by more than 9,000 votes to recapture the once solid Tory seat of Eastwood.
Colleagues praised Mr Robertson, who said it was the "responsible time" to step down now.
Sir Malcolm said: "I would like to thank Raymond for all his hard work. Being chairman of a party in Scotland or the UK is one of the most thankless and is an almost impossible task when your party is going through a period of extreme difficulty like ours is.
"It was never going to be easy and we owe him huge gratitude for what he has achieved."
There was some joy for the party when Peter Duncan overturned a Scottish National Party majority in Galloway and Upper Nithsdale.
Mr Duncan said: "We felt it was important that the people of Galloway and Upper Nithsdale should have a Conseravtive representative, and we have done that.
"We felt it was important that the Conservatives had voice in Westminster, we have done that.
"The people of Galloway and Upper Nithsdale overturned a significant nationalist majority and returned a Conservaitve and Unionist member of parliament. I believe out party has an important place in the United Kingdom."
The party's Elizabeth Smith came close in Perth - but lost out to the nationalists by less than 50 votes.
Mr McLetchie took some comfort from the Galloway gain, despite a 2% fall in his party's share of the vote with 70 seats declared.
That left the party in fourth place behind the Lib Dems for the first time.