Jones was unhappy with the award of the 86th-minute spot-kick - which was calmly converted by Lions striker Andy Keogh - but more upset by the application of his side.
The Owls, in search of their first win of the season, led for the majority of the game after defender Reda Johnson and winger Jeremy Helan cancelled out Kamil Zayatte's fifth-minute own goal.
"We should see it out, we should win the game," Jones said.
"We got caught with being the wrong side, (even though) it's not a penalty. The referee's closer; for some reason the linesman decides he wants to get involved and give it.
"We've watched it, we've watched it from every angle and it's not a penalty but that's not the reason why (we haven't won).
"The reason is because we should have seen out the game well before then. And, if we're not going to get the third, we certainly don't let them score.
"We didn't play well, we gave the ball away too many times. It's sloppy in our play but we got our noses in front. So when you're not playing well, you win it ugly and we didn't do that.
"I just felt certain players were half a yard off the pace. It was a very lethargic performance from a few players, who we can't afford to carry.
"We should just try and win the game ugly - okay it's not your best performance, so see it out.
"A player switches off, he gets caught the wrong side and then it's like a reaction and the linesman sees something no one else has seen, including the referee. But, it's our own downfall."
Millwall manager Steve Lomas was unsure about the award of the spot-kick, given after midfielder Richard Chaplow tumbled under pressure from Owls winger Helan, but felt his side were denied a certain penalty earlier in the game.
The result gave the Northern Irishman his first point and league goals since taking charge of the London club in the summer.
"I thought for long parts of the game we probably controlled it and got the ball down and passed it. Certainly second half we spent most of the time in their half, apart from the last five minutes.
"I think we started brilliantly and probably could've been two up.
"I've got to give the lads credit, they could've crumbled and gone under but they didn't.
"We continued to play our football and pass it about and try and probe for openings.
"I think the penalty was probably accumulation because the one earlier, (Jose) Semedo just rugby tackled Scott McDonald to the ground.
"I just don't know how the referee doesn't see that. He's the wrong side, he's got two arms around his waist. Maybe it's from that there that we get the decision, I don't know but I thought it was no more than we deserved."