The Potters needed a penalty shootout to beat the League Two side in the second round last night following a 1-1 draw after extra time at Kenilworth Road.
Mark Hughes's side will travel to Fulham for a place in the last 16 of the competition.
"It was a cup tie and one that we probably should have seen out in 90 minutes," Walters told Stoke's official website. "That's what they're about though; they're exciting particularly for the home fans here and I thought Luton equipped themselves very, very well.
"We should have done better at 1-0 up and we've probably switched off in the last few minutes. We can do better - we all know it - but we're through to the next round and that's the main thing."
Stoke resume their Premier League campaign on Saturday when they welcome West Bromwich Albion to the Britannia Stadium.