Fifth-from-bottom City head into the international break with a comfortable-looking buffer over third-from-bottom Barnsley, despite Saturday's poor home loss to Luton Town.
A 3-1 reverse to the promotion-chasing Hatters represented Hull's fifth successive defeat at the MKM Stadium and they currently possess the worst home form in the Championship, having lost 11 times in 19 matches, taking just 18 points from a possible 57.
In their final eight matches of the campaign, Hull must still face four more sides in the play-off mix in Huddersfield Town - who they welcome in their first game after the international break on April 1 - Middlesbrough, Millwall and Nottingham Forest.
Greaves said: "Barnsley have picked up a few wins and we have kind of given them a little bit of momentum and after beating us, they have gone onto have a few good results, drawing against Fulham after conceding in the last minute and winning the other night against Bristol City was a massive result and they have got themselves going a little bit.
"There's not much breathing space and we are going to treat every game like we have treated every game this season which is trying to go out and cause teams problems.
"We definitely still need a few more wins to guarantee our safety. But when you have guaranteed safety, you still want to go on and win games because you have still got things to play for and stuff like that."
A host of players are playing for their futures, with a number being out of contract. Talks with players' representatives are likely to be staged in the international break.
Greaves added: "It is a good position for the players to be in to want to try and show the people higher up that they want a new contract. I am sure that there will be talks with different players about contracts and stuff if they have only got this season left and they will be playing for their futures and that will help the team that they will be performing at their best to pick up a few results.
"Hopefully, that will get sorted with the players as this group of players have been important for the club. If we can get players tied down on contracts, that will be beneficial for everyone."