He remonstrated with the referee at the interval after Lee Gregory’s penalty in first-half stoppage time cancelled out Tom Bradshaw’s 40th-minute opener.
With Heckingbottom in the stands, Barnsley rallied and on the hour-mark Bradshaw found the net again, before replacement Mamadou Thiam wrapped up their first away win of the season with a late penalty.
“I made sure none of the players went up to the referee at half-time,” said Heckingbottom. “The staff’s job was to get them all away from the referee and I just approached him by myself.
“When I came out in the second half to go in the technical area he told me I couldn’t go in there. I didn’t want to make a scene, but I don’t know why I wasn’t allowed to be in there in the second half.
“It was a clean tackle (from Matty Pearson), we could all see it. When I watched it back it is so apparent with the Millwall players’ reactions, but the linesman’s flag went straight up.
“They were given the penalty before the referee could even make a decision. It’s just one of those things.
“I am delighted with the way we handled Millwall. We could control the game with the ball. The only blemish on it is conceding the goal and not keeping a clean sheet.”
Lions manager Neil Harris admitted the Tykes deserved victory.
Millwall: Archer, McLaughlin, Webster, Hutchinson, Meredith (Onyedinma 81), Wallace, Tunnicliffe, Saville, O’Brien (Ferguson 64), Gregory, Morison. Unused substitutes: Martin, Craig, Thompson, Romeo, Cooper.
Barnsley: Davies, McCarthy, Jackson, Lindsay, Pearson, Williams, Hammill, McGeehan (Bird 81), Potts, Barnes (Hedges 72), Bradshaw (Thiam 72). Unused substitutes: Fryers, MacDonald, Townsend, Ugbo.
Referee: O Langford (W Midlands).