Max Kucheriavyi’s late header sealed the title for hosts after Albion Rovers had shocked second-placed Annan Athletic at Galabank.
Swift said of the match: “The first half we were really good and we showed a lot of character to dominate the game.
“We expected an onslaught in the second half and they were well marshalled until the final moment.
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“It’s annoying we can’t just get it over the line at the moment, but I can’t be too critical of the performance.
“We let them score an easy goal but it was a very well-taken header and they are the side top of the league for a reason. They’ve got a squad that would match any side in the league above.”
He admitted his frustration lies with the fact the side above them, Edinburgh City, lost against Elgin City.
They are two points above the Warriors in the race for the final play-off spot.
“At this stage of the season, you do look to some of the other sides’ results,” Swift said.
“We are seeing that they aren’t winning every week, but we aren’t capitalising on that.
“That is certainly frustrating for everyone involved and it cannot continue.
“We can’t rely on Edinburgh and Stranraer to keep slipping up in order to get where we want to be.”