Global searching can be turned off using the option searching = FALSE, and you may also disable searching for individual columns using the option searchable in columnDefs, e.g. we disable searching for the first and third column:
library(DT)
iris2 = iris[46:55, ]
datatable(
iris2, filter = 'top',
options = list(
columnDefs = list(list(targets = c(1, 3), searchable = FALSE)),
pageLength = 5
)
)