Croatia striker Mario Mandzukic struck his third goal of the tournament against Italy who let their opponents off the hook after taking the lead and dominating the first half.
Bilic said a big problem in the early stages was that the Italians had too much space in midfield and took advantage of the gaps to create chances.
"I have to congratulate my team for showing the willpower and character to fight back in the second half," Bilic told reporters.
"We had a lot of problems containing [Mario] Balotelli and [Antonio] Cassano in the first half because our midfield was stretched against theirs but we adjusted our strategy in the second half and threw more men forward."
Croatia have four points from two games and Italy two points despite a refreshingly positive approach to the tournament.
The Croatian players said the win would only increase their confidence going into their final group match against Spain.
"We weren't good enough in the first half but we regrouped at half-time and in the second half we dominated and got a deserved equaliser," defender Vedran Corluka said.
"We still have work to do in our last group match against Spain but we are confident of progressing to the quarter-finals after this hard earned point."
Ireland face Spain in Gdansk in the other Group C match on Thursday.
