Jamie McGrath's brilliant strike looked set to earn the home side the win only for Livingston's Nicky Devlin to rifle in an 89th-minute equaliser to leave Goodwin frustrated on the occasion of his 40th birthday.
Speaking after the 1-1 draw, he said: "We can't be that nearly team. We have to keep believing and start to kill teams off.
"And most importantly managing the game better at the end and making sure we leave with three points.
"It wasn't a classic by any stretch, but it's just one of those you try to win and be grateful for the result. We couldn't do that unfortunately.
"We've had 14 games and drawn half of them and that's not good enough. We need to turn two or three of those into victories and that would make a hell of a difference to the league table.
"There were two fantastic goals in the game. Two great strikes. The awareness of Jamie to see the keeper off his line and provide that type of finish was a touch of class. And it's a hell of a strike from the Livingston player."
David Martindale felt his Livingston team were well deserving of the draw that extends their undefeated run to five matches.
He said: "I told the boys they deserved a point at least.
"It was a similar game when we played them at Livingston, we were unlucky not to take anything that day.
"This time it was two great goals that gets the point for the two teams. It could have been 0-0, we'd have been last on Sportscene - so at least there are two good goals to wait up for."
Despite the disappointment, Goodwin still hoped to enjoy the rest of his big day.
He added: "I had a great morning with my wife and my three kids, they spoiled me rotten. And we're going for a nice bit of dinner tonight. As fed up as I am at the moment, as soon as I see the kids' faces I'll be fine. I'll get a bottle of red and a nice bit of scran."