"They were excellent tonight, probably the best I have ever seen them play," Townsend told reporters after the Scots slumped to a chastening defeat.
"It's the reason why they are probably one of the two favourites for the World Cup.”
Scotland were overwhelmed in the first half at the Stade de France as Ireland raced to a 26-0 lead at half-time.
The Scots ran in two consolation tries in the second half as the Irish dropped their guard.
At the final whistle the Irish headed for a last-eight meeting with New Zealand while the Scots were left to reflect that they have failed to make the quarter-finals in three of the last four World Cups.
"Obviously It's a very disappointing result," Townsend conceded. "We've gone out of the World Cup against the number one team in the world.
"We believed we had the ability to beat them but they were the better team tonight.”
Townsend said his side had paid dearly for failing to take their chances.
"We just didn't convert... we got close to their tryline on a couple of occasions and we didn't turn that pressure into five or seven points," said the 50-year-old former Scotland star.
"It was a proper Test match in terms of both teams having opportunities for 20 minutes and they took theirs and they are very, very good at taking them.
"They're the best in the world for a reason.”
Townsend, who in May signed a contract extension until April 2026, was asked if the defeat felt like a "wake-up call" for Scottish rugby.
"You've got to look at each World Cup differently," he said. "We were drawn with the number one and number two teams in the world," he said, referring to Ireland and South Africa.
"We have to do better, we believed we could get out of this pool and we believed that after we lost to South Africa.
"If we can get on the journey (Ireland) have been on over the last few years, then great, but it's easy saying that, it's another thing doing it.
"We have to make sure this defeat makes us a better team.”
He admitted to casting an envious eye towards Ireland's rugby setup that produces a rich supply of talent.
"The players in this group and just outside this group are Test quality, but we have to get more players through," he said.
"The way Irish rugby is set up, they could dominate world rugby for five or ten years because they are the number one team in the world and their pro rugby system is very strong and they have got an age group system that's very strong.
"We've got to develop."