Manuel Pellegrini's men are winless in their last four games in all competitions, a run that has seen them cut adrift of favourites Chelsea, who they held to a 1-1 draw last weekend.
But the defending champions have secured each of their two league titles on the final day of the season and Kompany is adamant they are not worried by being behind with 15 matches still to play.
"This is just such a usual situation for us," Kompany said. "Five points behind in January or February? Big deal.
"We feel very comfortable, as we have been in that position many times before. We don't get over-excited, we don't get over-confident, and we don't get too desperate as well.
"We just have a job to do, and when we have to, usually we do turn up, so the team is ready for whatever happens next."
The hosts will be expected to at least maintain the gap to Chelsea - who travel to Aston Villa on the same day - by beating a Hull side scrapping to avoid relegation to the Championship.
Steve Bruce's team went down with a whimper in their 3-0 home loss to Newcastle United, a result that kept them in the relegation zone, a point adrift of safety.
With just four league wins to their name all season, the pressure is mounting on Bruce, but reports in the local media have indicated that he will not be sacked despite rumours to the contrary.
Bruce will hope that the addition of Senegal striker Dame N'Doye can make a difference after he joined the Yorkshire club on a two-and-a-half-year deal from Lokomotiv Moscow.
Hull have no new injury worries heading into the trip to the Etihad Stadium, although Liam Rosenior (hamstring), James Chester (shoulder), Mohamed Diame and Robert Snodgrass (both knee) remain on the sidelines.
Meanwhile, Pellegrini is still unable to call on January signing Wilfried Bony, who is set to feature for Ivory Coast in the Africa Cup of Nations final on Sunday.
Yaya Toure will captain Ivory Coast in that clash, but another playmaker, Samir Nasri, is in contention to make his return.
Nasri has been out of action for the last four games because of a calf complaint, while defender Eliaquim Mangala is also line to make a comeback from a groin problem.
