"The confidence is back with the points we are taking and we don't want it to stop," Bilic told a news conference on Thursday.
"We have to continue to play like this."
Leicester, by contrast, are having a torrid season, and Monday's 2-0 home defeat by Everton sent them down to 16th place, just three points above the bottom trio.
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Bilic, whose team have been boosted by the return to training of defenders Sam Byram and Reece Oxford, and midfielder Manuel Lanzini, backed last year's champions to eventually turn their season around.
"Leicester are not happy about their position in the Premier League but they have the quality and the resources. They should be alright," he added.
The manager shed some light on his transfer plans for the January window, indicating that he would look within the league for reinforcements rather than abroad.
"We are the club who are linked with most of the players in Europe," he added.
"We want players who have experience in the Premier League. We are not going to panic and will try and get a couple of players."
(Reporting by Simon Jennings in Bengaluru, editing by Neil Robinson)
