GB now have one victory and one defeat to their name following their stunning 3-1 win over top seeds Slovenia on Sunday.
Luke Ferrara gave Britain an early lead but Kazakhstan scored six unanswered goals to secure their second victory at the tournament.
"There is no shame in losing to Kazakhstan and I didn't think it was a 6-1 game," said the Sheffield Steelers forward.
"They are a really good side and they punished us on the powerplay where they were lethal.
"I felt we had periods where we more than matched them, so we can take plenty of positives."
GB return to action tomorrow when they face Poland in their third game of the tournament.
"We match up well against Poland," continued Phillips. "We always have great games with them.
"It will be an intense battle and we know they will come out hard, but we are ready for the fight."
GB against Poland gets under way at 4pm tomorrow (3pm UK time).
*Forward Luke Ferrara says he will never forget his first GB goal as he found the net in only his second World Championship appearance.
The 24-year-old gave GB an early lead against Kazakhstan before the tournament's second seeds came back to secure a 6-1 victory.
"It was a very special moment and I won't forget it," said the Coventry Blaze forward.
"I thought we started the game really well and for the first 10 minutes we dominated the game.
"I wish the goal could have been part of a winning scoreline, but we can still take positives from how we played.”