And he told the BBC that the party must strengthen its political organisation before the 2003 Scottish Parliament elections.
The SNP held five Westminster seats, but was the only party in Scotland to lose a seat when the Tories took the Galloway and Upper Nithsdale constituency.
" We have established ourselves as the principal opposition party in Scottish politics "
The party also saw its vote fall by more than 150,000 from its 1997 general election level.
Mr Swinney told BBC Scotland's Campaign 2001 programme that Labour and the Tories had also seen their share of the vote fall - and stressed that the SNP was now established as the main opposition north of the Border.
He said the party had fought a "very professional" campaign and delivered a clear message.
But he admitted: "There are things we need to do to strengthen our political organisation on the ground to make sure that we have the fighting ability in every constituency to win political leadership.
"That is one of the important aspects of my leadership that I am going to turn to, to make sure that we have that political organisation in place.
"I obviously would have liked the SNP to have made more progress in this election campaign, but I can assure you that the SNP comes out of it having learned a great number of lessons and determined to win political leadership in 2003."
He admitted to his disappointment at losing the Galloway seat to the Tories.
"But what we faced in this election campaign was the challenge in motivating people to vote in elections for Westminster, when quite clearly people see the SNP primarily relevant to the Scottish parliamentary elections," he said.
He said Labour had been placed on probation by the voters and promised that the SNP would hold the government to account in the 2003 Scottish election campaign.
And he added: "We have established ourselves as the principal opposition party in
Scottish politics, and that is a position to advance on towards the 2003