Wanderers had taken a first half lead after Seagulls midfielder David Lopez steered a Chris Eagles corner into his own net, but Brighton hit back with three goals in four blistering second half minutes.
Jay Spearing headed a Kazenga LuaLua free-kick into his own goal to bring the home side level, before Inigo Calderon and Will Buckley both added goals as Brighton stretched their unbeaten league run to six matches.
Freedman admits that speculation surrounding his future at the Reebok Stadium is deserved, but insists that the pressure does not faze him and that he is the man to turn the club's fortunes around.
"I think my job is very safe. I don't ignore speculation surrounding my job but I don't feel the pressure of it," said the Bolton boss.
"When you've been in the game for so long you learn to deal with speculation about being sacked. It doesn't faze me at all and it's my job to take the blame away from my players.
"I understand more than anyone exactly what we have to do to turn things around. We need a couple of players in on loan and time to gel as a team."
Freedman believes four "crazy" minutes in the second half cost his team a point and bemoaned his players' lack of concentration after the restart.
He added: "Apart from four crazy minutes in the second half there's absolutely nothing in that game. The first goal was the killer. If we had kept our concentration then, things could have been different.
"We need to be more determined. Our communication let us down but these players showed last year what a win will do - if we can get that first victory under our belts, I'm confident we will go on a run."
Delighted Brighton manager Oscar Garcia saluted his side's second half fight back and stressed the importance of the victory after consecutive stalemates against Reading and QPR.
The Seagulls are unbeaten in the league since early season defeats to Leeds and Derby and Garcia praised the second half finishing of his players after a wasteful first period.
He said: "It was a very important win for us. It was important more than anything to get three points after the draws at Reading and QPR.
"I told the players at half-time that that we needed to be more clinical. We lacked a killer instinct in front of goal despite a lot of pressure in the first half.
"When you play at home there is more pressure, more expectation, so I am pleased for the players because we have many injury problems and it has made it difficult for us."
Garcia offered support to opposite number Freedman and urged Bolton chairman Phil Gartside not to sack the 39-year-old Scot.
He added: "They were the toughest team to play at the Amex this season. I am not the Bolton chairman but it is clear they need time to gel because they have a lot of new players.
"They have a very good squad and a fantastic manager. They didn't look like a team that were bottom of the table and it was hard for us. I know with time that he [Freedman] can turn things around."