Since replacing Mark Hughes, Lambert has guided Stoke to five points from four matches in the top flight, although the Potters have not won any of their last three games.
Stoke make the short trip to the East Midlands to face Leicester City on Saturday, and Lambert has backed his side to cause a surprise at the King Power Stadium.
At a press conference, the 48-year-old told reporters: "I'm delighted with the effort they've shown in training and games. We've looked as though we can win games and we look as though we can really compete, which is really pleasing.
"From the day I came in, they grasped pretty quickly what I wanted and what we're looking for. There's not been a time where I've walked away from training or a game thinking we're not at it.
"If we can keep the level we're and add a wee bit of luck in front of goal we can certainly win games."
Stoke currently sit in 19th place in the Premier League table, two points adrift of safety.