Connacht took control of the game when Niyi Adeolokun touched down following a penalty for each side before an unconverted Leone Nakarawa try got Warriors back into the game in the second half.
Two more AJ MacGinty penalties were enough to give Connacht the win in a bruising encounter.
Connacht will meet Leinster at BT Murrayfield in Edinburgh on Saturday in their first ever PRO12 final against the club that have claimed the title the most times.
"I'm extremely privileged and blessed to be part of this group and represent the west of Ireland," said Lam.
"It's just a magnificent day for the west of Ireland. We have fantastic support here and we know there were so many people who wanted to be here at the game who couldn't be.
"Sligo, Leitrim, Roscommon, Mayo, Galway, right through; it's just a wonderful day for the west of Ireland.
"It's not only a great day for the west of Ireland but a great day for Ireland. We have an all-Ireland final next week and it's going to be great. It's a good day."
Lam was quick to turn his attentions to next week's final against Leinster who they beat 7-6 at the Sportsground in March having been beaten 13-0 on New Year's Day during the regular season.
The head coach believes there's plenty to do to prepare his side for an experienced Leinster side full of Ireland internationals.
"The thing about the review on Monday - I've got a bit of work to do tonight - the thing is that the players need to understand how we won," he said.
"Most of the answers are our team structures and systems and what we do.
"The next thing on Monday is that the players need to know exactly how we're going to beat the next team and how we go about doing it. That gives them the whole week to prepare.
"They've been there and done it. If we try to match them individually, we'll get blown off the park.
"But as I said to the boys, it's going to come down to our team structures on attack and defence."
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