"It was tumultuous. Exhausting. I'm delighted on behalf of the team. I spare a thought for England, they were superb today and probably deserved a share of the spoils," the 49-year-old New Zealander told the BBC.
"I'm looking forward to being quite relaxed now. Hopefully we can keep going forward.
"Days like today build coronaries for coaches. But it also builds character. We're delighted and relieved."
Schmidt's England counterpart Stuart Lancaster was desperately disappointed at once again seeing the title elude his grasp - Ireland edged them also on points difference last year with a final win over France in Paris.
"I'm gutted really. It was one of the most courageous performances I've seen from a team," Lancaster told the BBC.
"Credit to Ireland, they beat us away from home, so congratulations to Joe Schmidt and his team."
For Ireland's iconic captain Paul O'Connell - who scored a rare try in the Scotland game - it was surreal to accept what was a replica trophy, the real one having been deposited at Twickenham.
"I never would have predicted such a game at Twickenham," the 35-year-old lock told the BBC.
"Fair play to England and fair play to France. I've never received a trophy in such a bizarre situation. It's strange. In some ways it's better than last year."
O'Connell refused to say whether this would be his final Six Nations match.
"I hope not."
O'Brien's tries - one in each half - helped the Irish pass Wales on points difference after the Welsh had humiliated Italy 61-20 earlier in Rome with wing George North getting three tries.
Earlier, North had sparked Wales to a stunning second-half performance against an all at sea Italy, who had given them a good game in the first period.
Wales coach Warren Gatland had been looking for a win of over 40 points and he got it as the Welsh sprang into action after leading only 14-13 at half-time in Rome.
Their victory - helped by Italy being reduced to 14 men on two occasions - ended France's slim hopes of the title as the Welsh went to eight points, the French could at best have finished with six by beating England at Twickenham.
Gatland regretted the last minute converted try by Italy that could have been decisive.
"It wasn't bad apart from the last two minutes!" Gatland told the BBC.
"You are always looking for the perfect performance," said Gatland.
England ran in seven tries to France's five in a stunning final match of the tournament but despite battering away at their visitors line late on, could not manage one more converted score needed for overall victory.
- AAP
