The 30-year-old opened the scoring on the half-hour mark but saw his side pegged back as Paulo Gazzaniga failed to keep a Robert Snodgrass free-kick out.
And the forward admitted Saints left the field disappointed by their inability to kick on from there as the game ended 1-1.
"I am definitely frustrated not to get the three points," Lambert said. "I thought we played really well in the first half and I thought we were definitely going to win it.
"We've come in disappointed at half-time and felt we could have pushed on in the second half.
"We haven't managed to do that so, yeah, I am disappointed."
Lambert's opening strike was shrouded in controversy due to an alleged hand ball in the build up, with referee Mark Clattenburg ignoring Norwich appeals on his return to officiating.
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"I am not sure exactly where it hit me but obviously I just carried on and put it in the back of the net," he said.
"Obviously I am just looking at the ball, it's hit me and it has landed there. You've just got to play to the whistle."
The 30-year-old was also quick to defend rookie goalkeeper Paulo Gazzaniga, who seemed at fault for allowing Robert Snodgrass's equaliser to slip through his arms and into the back of the net.
"He didn't have to apologise to us," Lambert insisted. "You could see he was disappointed.
"He has done really well the last few weeks and it was a just little lapse in concentration.
"He is more disappointed than us and these things happen. It is how you respond to it."