A wonder strike from Kallum Higginbotham just five minutes from time looked to have sealed the three points for Partick Thistle, but substitutes Tony Andreu and Jason Scotland secured Hamilton their third league win in a row in the dying moments of the game.
And Neil believes Accies side, who were promoted after overturning a first-leg playoff deficit against Hibernian, have good into the habit of not knowing when they are beaten.
"I'm really pleased," Neil said. "For a start, I thought it was a really good, competitive game with both teams really going at it and there were some good opportunities.
"The first half was pretty even, I thought we had chances and they had chances. Second half, I thought we controlled the ball more, I thought we put them under more pressure, and they took the lead against the run of play.
"We had just been up the pitch and Ali Crawford has missed a great chance to put us 1-0 up, they score, and it sort of kicks you in the gut a wee bit.
"But the resilience and the character that this team has shown over the last year that I've been with them has been nothing short of remarkable, and we showed it again today.
"I thought once we got the goal, I know what the team is capable of, and if you come and watch us on a regular basis - certainly last season we were 2-0 down at Cowdenbeath and came back to win 4-2, the Morton 10-2 game, the Hibs game away when we were 2-0 down - we've done it so many times so it's not as if it's a fluke.
"We're capable of doing it, and the goals we scored, as far as we're concerned, were quality goals."
Thistle boss Alan Archibald reckons Hamilton were dangerous throughout the match, and claims he never felt the match was won when Higginbotham scored.
"To be fair to Hamilton, they were the better side I thought at times," Archibald said.
"Even though we've created a number of chances to go on and win the game and scored a wonder goal with five minutes to go that should have been enough to go on and win the game at home.
"I didn't celebrate the goal because there was still five minutes to go and you always know what's round the corner at times.
"When you've just scored that can be your most vulnerable time, but the boy's ran 40 yards with the ball and he should have been stopped before then."