Peter Houston has told his Falkirk players they will need to improve if they are to finish the job of beating Kilmarnock and gaining promotion.
His side opened up a 1-0 advantage in the Premiership play-off final first leg, Will Vaulks scoring late on.
But Houston insists it is still all to play for when the sides meet in Sunday's return leg at Rugby Park.
"We were fortunate to win. There's so much work to be done," Houston told BBC Scotland.
"I don't know if that's Kilmarnock's best shot, but we can do better, we can pass the ball better, we can take more care of the ball."
The game looked destined for a goalless draw before Luke Leahy took a quick free-kick to Craig Sibbald, who teed up Will Vaulks for the winning goal in stoppage time.
"I was disappointed that our good players never passed the ball well enough," admitted Houston, whose side finished as Championship runners-up.
"There were lots of lessons for our players to learn. I felt we let Kilmarnock bed in better than us, they started brighter than us, and we've got our goalkeeper to thank for making a great save in the second half."
Kilmarnock ought to have scored through Tope Obadeyi, but he sent the ball into the side-netting after rounding Falkirk goalkeeper Danny Rogers.
Kris Boyd also might have scored for the visitors, his header blocked by Rogers, and Killie must overturn their deficit to avoid relegation from the top flight.
Kilmarnock manager Lee Clark was frustrated by the chances his side missed, but also for not being awarded a penalty in the first half when Obadeyi appeared to be impeded by Leahy, but did not fall to the ground.
"My player's been fouled, but he hasn't gone down," Clark said. "A foul's a foul, whether he goes down or not.
"I try to get my players to do the right thing but do they have to go down now to get penalty kicks? I don't want to advocate that to my players.
"We're disappointed to be a goal behind, because for long periods of the game we were the dominant team. But we've got to dust ourselves down and go again and score two goals at least.
"I'm frustrated. I would have been okay with a 0-0, I came here to win, but to be behind to a goal like that is terrible.
"It was a dreadful goal from our point of view, no excuses for that, it was unacceptable. You're in injury time, you get all shirts back to defend your goal.
"We've shown that we had a lot of quality at times, we opened them up and we needed to finish them off."