Davies missed the penalty, but the Trotters hung on to give Lennon a winning start.
The former Celtic boss told the Bolton News: "I got sent off because [fourth official Amy Fern] said I was consistently leaving my technical area. What I wanted to do was get the message on to Jay Spearing to take the penalty.
"By all accounts Craig has scored the last three but I wanted a technical player to go up and take it, put his foot through it and put the game beyond doubt.
"In the end he's blasted it over the bar against an outfield goalkeeper. That tells me our game management needs to be a lot better."
The result has moved Bolton off the bottom and up to 23rd in the Championship table.