Saturday’s stalemate at Leigh Bent sees Falkirk fourth in the Tennent’s National Division 2 table with 15 points from four matches.
Falkirk director of rugby Kenny Grieve told the Falkirk Herald: “We were under the cosh the first 15 or 20 minutes.
"They came out the blocks really, really hard and we couldn't get a foothold in the game at all.
"It took us 20 minutes to get there. The fortunate thing for us was that they probably expended 40 minutes worth of energy in the first 20 minutes.
"Our greater fitness obviously came through and we then managed to get a foothold in the game and then from there we dominated the rest of the first half which was pleasing and we got back to leading at half-time.
"We can’t afford to give teams a 17-0 head start and we did it the week before when I think we were down 22-7 against Gordonians.
"So it’s something we need to work on and get better at if we start kind of slow. Once we get into the game we’re pretty good.”
A penalty and two converted tries did the damage for Bulls early on, before Falkirk reduced the deficit to 17-7 when they capitalised on the hosts having a man sin-binned to score through Gregor Dodd with Duncan Tompkins adding the conversion.
But Hamilton then scored in the corner to go 22-7 in front, before Falkirk tries by Cameron McKenna and Gregor Brodie – the second of which was converted by Tompkins – reduced the visitors’ leeway to 22-19.
Stef Yarrow then carried over from close range – conversion was good – to put Falkirk 26-22 ahead at half-time.
Into the second half and a Tompkins penalty extended Falkirk’s lead to seven points, before a converted try for Bulls levelled matters.
Andy McNabb then scored on his return to Falkirk’s 1st XV after being out injured for nearly two years and the Tompkins conversion made it 36-29 for the away team.
A Hamilton try brought them within two points before a Tompkins penalty made it 39-34 for the visitors.
Bulls earned a draw late on with a last play score, conversion missed.
Grieve added: “We were pretty dominant in the second half but we got caught very narrow at times.
"So we’re going to work on our defensive line and our energy getting off the line and getting to the contact point this week at training. Hopefully we will improve for this weekend.”
Falkirk’s next league outing sees them at home to Glasgow Accies this Saturday, KO 3pm.
"Glasgow Accies are another side who’ve not had the best of starts,” Grieve said.
"They have already played high flyers GHK and were narrowly beaten on Friday night.
"So again it’s a tough test. There’s no easy games in this league but it’s about what we do.
"Every team on their day is capable of beating everyone else.
"If we play to our potential we should manage to beat them.”