However, the result looks to have come at a cost for the Clarets, after the FA deemed an off-the-ball elbow from Tarkowski on Murray in the 35th-minute as worthy of a 3-game ban.
The pair clashed in the 35th minute of their goalless draw at the Amex Stadium on Saturday.
In its statement announcing the charge on Monday, the FA said Tarkowski had until 6pm on Tuesday to respond.
Brighton and Hove Albion manager Chris Hughton is concerned about his side's lack of goals in recent games but says his forwards are confident of turning things around.
Each panel member will review the video footage independently of one another to determine whether they consider it a sending-off offence.
For retrospective action to be taken the decision of the panel must be unanimous.
Tarkowski, whose form for high-flying Burnley has resulted in him being touted for a first England call-up, would miss Premier League matches against Tottenham, Manchester United and Huddersfield Town over the busy festive period.
"I think a lot of people think it's two points lost but we work on 40 points keeping us in the league". I'll be careful with my words now, but there have been some interesting cases recently.
"It's the area we need to improve the most". I'm big on simulation, and it's going on all across the pitch across the league.
'You have to be careful, if you're going to start opening everything up, I'd start with simulation.
"All you can do as a team is try to stay focused, try to keep the momentum we had at the time and try to score a goal from open play to release that bit of tension".