Their current 12-point lead at the league's summit gives them the ideal cushion and a bonus point win on Friday night - away to Edinburgh - would be enough to get them over the finishing line.
Dempsey said: "We are in a strong position in the league now and while there are some who might feel that we can take our eye off the ball, you can't afford to do that in this competition where all the teams are so strong.
"Over the last five or six weeks, we have taken each and every test on an individual basis, and as Michael Cheika says, we're treating each and every game as a cup final.
"We're targeting each game as a win, because we want to create a winning culture in the squad."
Dempsey was hugely encouraged by last Saturday's 21-12 win over Munster at a packed out RDS where the blue-clad Leinster certainly made their voices heard.
"Last weekend was by far the best atmosphere we've ever had at the RDS," the Ireland international explained.
"Standing at full-back you could hear the Munster supporters trying to sing their songs and they were just drowned out by our support and all the flags and colour gives you such a lift when you're out there.
"The support that we've been receiving over the last few years is really coming together - both at home and on the road - and the impact is becoming more noticeable.
"I hope the supporters come over and cheer us on again in Scotland. Murrayfield can be a bit hollow at times, and any advantage we can bring can only be a good thing."
Back fully fit after time out with a hip injury, Dempsey was 'delighted' to start against Munster last weekend as he admitted 'it's so frustrating when you're out on the sidelines looking in.'
"Games like the Munster one and Edinburgh on Friday are the ones you want to play in," he added.
"As the league draws to a close we need to have as many fit players, and players on form especially, as possible."
Form is something which has been oozing out of the Leinster squad in recent weeks and months. Since their Heineken Cup exit in January, Cheika's side have really knuckled down and got some excellent results.
In all, the province have won ten league games in a row and the consistent efforts of their oft-criticised pack and emerging young players have really driven the team on.
"The pack have received a lot of praise this season, and rightly so, in my opinion," Dempsey insisted.
"They have set down a platform from day one and have worked incredibly hard and it's a pleasure to play alongside them.
"I look across the back-line now and the really encouraging thing is that we have such a young panel.
"People forget that Luke (Fitzgerald) is only in his second season, Rob (Kearney) is only in his third and then you have someone like Jonathan Sexton calling the shots and really producing top class performances.
"He's well able to boss a game and he, like many others, is showing great leadership and maturity.
"Great credit has to go to their work ethic and their mindset because I know how hard it can be trying to establish yourself.
"They're all a breath of fresh air and there are a lot more talented players also coming up from the Academy.
"It's an exciting time to be with Leinster and it's good for everyone that the level of competition is so strong," he added.
The 32-year-old knows full well that Edinburgh have been something of a bogey team for Leinster, with last December's 29-10 defeat to the Scots scuppering Leinster's Heineken Cup quarter-final chances.
Edinburgh also beat the Irishmen twice previously in the pool stages of the Heineken Cup, 29-21 in 2000 and 25-24 in 2006.
Dempsey, who played in all three of those defeats, said: "I know our recent record in Edinburgh hasn't been too good, but people forget that they play very well at home.
"They're a good side and they don't get the respect they deserve. They're a very strong outfit, they chase you down and never give up.
"They're not afraid to throw the ball about and we know that they will fight to the very end.
"For us though, Friday night is a new game. We're starting afresh and focusing on this upcoming game on an individual basis."