Accies took the lead through Simon Mensing with Martin Canning seemingly in an offside position.
Referee Willie Collum dismissed Celtic’s James Forrest and Hamilton’s Jim McAllister after the break.
Mensing also saw red for a foul in the box, Anthony Stokes converting from the spot before having a goal disallowed deep into injury time.
The Parkhead side now sit five points clear of arch-rivals Rangers, but the Ibrox side have three games in hand.
Celtic had the bulk of possession in the early part of the game, but found it hard to break down the Accies rearguard with the home side pressing Celtic players whenever they were on the ball.
IT had all BEEN happening off the pitch at Celtic – with the club drawn away to Rangers in the Scottish Cup…and Neil Lennon handed a six-match touchline ban by the Scottish Football Association for an excessive misconduct charge.The ban begins on 18 January, meaning the Hoops boss will be absent from the dugout for the Cup game on February 5 of 6.
Celtic will appeal the decision – being seen in some quarters as further evidence of an anti-Celtic bias in the SFA.
“We are very surprised and extremely disappointed,” said Celtic in a statement on the club website.
“We believe the punishment is excessive and unprecedented for a first offence.”
Lennon was given the ban for being sent to the stand by referee Craig Thomson during Celtic’s 2-0 defeat by Hearts in November.
That dismissal – following an altercation with fourth official Steven McLean – incurred an automatic two-match ban, which Lennon was appealing at Hampden on Tuesday.
Celtic’s statement added: “We have maintained for some time that a range of the SFA’s processes and structures needed to be reviewed and updated.
“This view was supported recently by Henry McLeish in his review of the SFA.
“Tuesday’s events only underline and reinforce our opinion.
“Without question Celtic will be supporting its manager Neil Lennon in his appeal.
“As well as challenging the severity of the punishment imposed, our appeal will also focus on issues of procedural fairness and the manner in which such hearings are conducted.”
The first match of the ban will be the Scottish Premier League visit of Aberdeen on 22 January.
It will take in two more games against the Dons, meetings with Hearts and Dundee United, and the Scottish Cup fifth-round trip to Ibrox.
If the appeal fails – and the SFA are unlikely to climb down – Lennon’s first game back on the sidelines will be Old Firm league clash with Rangers at Celtic Park on 20 February.