Bundee Aki's late try sealed a first victory at Thomond Park for Connacht since 1986 and moved them four points clear of their Irish rivals at the top of the standings.
And Lam insists his troops must start to feel like this is where they belong if they are to extend their fine start to the campaign.
"I am tremendously proud. I love history and I respect it because it tells you where you come from, but the vision decides where you are going," Lam told Sky Sports.
"When I arrived at Connacht, a lot of people told me where they are and where they belong and so forth, and the first thing we needed to remove was the chip on the shoulder.
"It is all about what we can do and what we can create here. We are a professional team and I just said to the boys that at the end of the day what we did out there was what we do every day at training - today is no different to what we did last week against Brive or what we did in Russia.
"We have put a lot of work into skill development and making sure that guys can pass, catch under pressure, that they can run good lines and that everyone can look after the ball at the breakdown.
"We got four points out there but we still will go through the process of what did we do well and more importantly what we can do better.
"We will go through that on Monday and we have a short turnaround for Cardiff next week."
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Guinness PRO12 Connacht News
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