Gordon Reid's second-half score brought Warriors back from Bundee Aki's try and a 7-0 deficit, but Tiernan O'Halloran was on hand to put Glasgow away with a try on his 100th appearance for Connacht.
Leinster's crushing 50-19 win over Benetton Treviso and Ulster's 46-26 win away at the Ospreys mean the two Irish provinces will meet again in the other semi-final, but Glasgow's Townsend is confident his charges can reach a third consecutive showpiece by becoming the first away side ever to progress to a Guinness PRO12 final.
"I'm a big believer in what this team is capable of. They will have learned a lot today," Townsend told BBC Scotland.
"It's a case of who learns the most between now and when we come back in two weeks, and who puts in a performance full of effort, energy and intelligence.
"We will be determined to play better in a couple of weeks. We made more mistakes than we have been in recent weeks. Part of that is down to the weather; it was tough conditions, but we have to play the conditions slightly better.
"The effort was excellent and I was proud of the way we came back at the end and almost got the draw that would have got us back home in the semi-final.
"Connacht knew they were in a game, but I am sure they will be better in a couple of weeks too. So we have just got to make sure we are better than them."
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