The Tractor Boys produced an upset 1-0 winning performance over Premier League outfit Arsenal at Portman Road on Wednesday night, surprising many onlookers.
Norris was jubilant after the win but knows that Ipswich still have it all in front of them before they can relax.
"I think pretty much everyone in the country wrote us off today so we've surprised a lot of people," he told Sky Sports 1.
"We let a lot of people down against Chelsea. We didn't do ourselves justice so we went out tonight with that bit of extra determination and did what we had to.
"But there's still work to be done and we still have to go to the Emirates in the second leg."