Erik Edman was adjudged to have handled in the area at the start of the second half and El Hadji Diouf slotted the spot kick for 1-0.
Jermain Defoe levelled after 68 minutes but Fredi Kanoute was sent off 60 seconds later for a second bookable offence.
Few chances were created in the final 20 minutes until Bolton grabbed two goals in a minute just before full-time to clinch a 3-1 victory.
However, the penalty was a key decision and Allardyce said: "It his his arm and the referee has to decide whether it's arm to ball or ball to arm.
"In his opinion it was arm to ball and we got the decision.
"We had the same referee for our game against West Brom and I felt we had a blatant handball that day. He didn't give that one, he did this one and it helped us on our way to the victory.
"Just as you get into the habit of losing, so you can get into a habit of winning.
"We feel that no matter what happens we are not going to lose at the moment and that's down to the hard work of the team and our determination not to concede a goal.
"That's the main reason why we are shooting up the league. As a team we have shifted our mentality from being attack minded to not conceding.
"Some of the bounce of the ball and rub of the green is now going in our favour and we are capitalising on it."
You got the impression that Bolton boss Sam Allardyce felt some sympathy for us after his side's controversial penalty award.