Tailenders Umar Bhatti, Anderson Cummins and Henry Osinde were all run out in comical fashion as outsiders Canada were dismissed for 199 before Kenya won the Group C opener by seven wickets.
"Yeah it was pretty village, wasn't it?" Davison told reporters. "It was pretty embarrassing at times. There weren't too many positives there for us."
Kenya captain and man-of-the-match Steve Tikolo, playing in his fourth World Cup, said his 72 not out and two for 34
"It is important being a senior member of the team you try to lead from the front," the 35 year-old said. "It's important to win the first game to get the momentum. I believe in my players."
New Zealand play England on Friday before Canada face England on Sunday and New Zealand clash with Kenya on Tuesday.