The Hammers are currently languishing in the bottom three of the Premier League having won only one of their opening six games.
Following their impressive 17th-placed finish last season, Bilic’s side have disappointed thus far with some supporters blaming the switch from Upton Park to the London Stadium.
Yet Karanka, whose side visit the London Stadium on Saturday, believes the Croatian will turn things around.
“They are not in the best moment, but they are a good team, they have a good manager,” he said.
“They had an amazing season last season, so our biggest mistake would be to go to play against West Ham thinking that they have problems because they are not winning games.
“They are going to start winning games and I hope it’s not on Saturday.”
Boro are sitting just two points above the East Londoners, despite taking an impressive five points from their opening three games.
Karanka has urged his players to raise performance levels in order to halt their current three-game losing run.
The Spaniard added: “”We played really well against Everton and when we played with our intensity and our consistency and the right attitude, we were at least as good as Tottenham, and we are speaking about a team which is playing in the Champions League and is unbeaten in the Premier League.
“We have to keep going in that way. We are learning, but we have to learn quickly because the games are going and we are losing games.”