"We were relentless with our pressure in the second half and I'm just so disappointed for the players. The only thing that beat us was time.
"The one thing I will say is that, while I'm the manager, there is no way this team is going under. No way."
The Bairns remain one point adrift of Kilmarnock at the foot of the Scottish Premier League after Marco Paixao headed the only goal in a first half dominated by the visitors.
Falkirk turned in a spirited performance after the interval and came close to an equaliser when Darren Barr's header cannoned off a post.
We play St Mirren next week and that's as far as we'll look. We have to win that game; no doubt about it
Falkirk manager Steven Pressley
"I think, if we'd gone on for another 10 or 15 minutes, there's no doubt what the outcome would have been," said Pressley, who refused to criticise the limp performance of his side in the opening 45 minutes.
"It was a relatively even first half, with both sides having a number of chances," was his verdict.
"Hamilton are a very good side; they have proved that over the course of the season.
"But I thought, in the second half especially, our performance was excellent. We really did perform in the manner which makes you proud as a manager."
St Mirren, who are four points better off than Pressley's team, visit Falkirk next weekend and the manager is targeting a victory.
"We'll be ready, we'll be coming out fighting and we are very much up for the challenge ahead," added the former Scotland defender.
"Every single week, these players have given me their lot and everyone is aware of what's ahead of us.
"There are no heads down. We spoke in the dressing-room and we know what we are all about.
"We play St Mirren next week and that's as far as we'll look. We have to win that game; no doubt about it.
"We had a terrific performance against them three weeks ago, winning 2-1, and we'll be looking to repeat that."
Source: BBC Sport
Source: BBC Sport