England needed to beat France by 26 points at Twickenham in the final game of the tournament but only managed a 55-35 victory to leave Ireland as champions.
"It's going to be the death of me, it was pretty tough viewing but all of this makes it worth while. The people that have stayed here represent a fantastic support base that we have," Ireland coach Joe Schmidt told Irish television.
"We were only just glued together towards the end there because the English really put the pressure on, I'd certainly sympathise with them a little bit. I though their performance today was superb.
"Thankfully France rebounded each time England did get a bit of a differential and that allowed us to hang in and hang on to the silverwear," Schmidt added.
"I'd love to say I've got something to do with it but I think Paul O'Connell grabbed the week by the stuff of the neck, grabbed himself by the scruff of the neck by about Tuesday afternoon and he led them forward."
Ireland captain O'Connell crashed over from close range to score an early try and flanker Sean O'Brien surged across the line to put the visitors 17-3 ahead.
But Scotland regrouped and flyhalf Finn Russell scampered over in the left corner to reduce the deficit to 20-10 at halftime.
Ireland dominated possession and were rewarded when centre Jared Payne scythed through the Scottish defence to touch down with Scotland in chaos.
Scottish hopes took another hit when prop Geoff Cross was sent to the sin-bin but Ireland flyhalf Jonny Sexton missed two straightforward penalties.
Sexton re-adjusted his radar, however, to extend the Irish lead to 33-10 and man-of-the-match O'Brien burrowed over from close range seven minutes from time.
Scotland fullback Stuart Hogg failed to ground the ball over the line under heavy pressure from Jamie Heaslip and although Ian Madigan missed a late penalty to extend the lead, Ireland were left to celebrate their record victory at Murrayfield.
Scotland's fifth successive defeat in the tournament left them bottom of the Six Nations standings after another depressing campaign.
