Joe Schmidt's men had led by 11-points at the interval at Thomond Park but suffered heartbreak, with a last-minute Ronan O'Gara penalty snatching a 24-23 for fierce rivals Munster.
And Hines, who pulled on the Lions jersey on five occasions during the tour of South Africa, insists his side's Heineken Cup dreams will come crashing down at the Aviva Stadium unless they are more street-wise in the quarter-final against Leicester Tigers.
"They do what they do, and if we're not more accurate and effective than we were last weekend then we could end up on the end of the same result," Scottish back-five forward told the Irish Examiner.
"It's a pressure game, isn't it? They've got extremely effective forwards, a strong front five and a pretty quick and mobile back row.
"If they get any sort of ascendancy up front, then they have got Toby Flood, a good distributor, and good runners off him."
Now Hines has called on the Leinster pack to front-up against the Tigers and provide a solid platform for victory.
"Against Munster we lost a little bit of momentum. We were a little bit inaccurate. I got turned over by O'Gara, of all people and we didn't run out.
"We lost a bit of shape. Just bit by bit, Munster got back into the game, got a couple of penalties that relieved a little bit of pressure and they kicked some penalties as well.
"Leicester bring their physicality every weekend. We have to fight fire with fire and on a couple of occasions we have done it this year. We've just got to make sure we bring that intensity this weekend."