The champions of last season are 14th after 21 games, 12 points off fourth place and just six clear of Sunderland, who occupy the final relegation place.
The Blues’ predicament prompted Jose Mourinho’s departure last month and Hiddink’s appointment.
Chelsea are unbeaten in six games since Mourinho left, when they were one point off the drop zone, but the midweek draw with West Brom did little to ease concerns.
“It’s reality,” Hiddink said. “We were down when we started. We were one point off the relegation line, but now we have a little bit more room to breathe.
“We have two difficult games coming up — Everton, who have a very good away record — and then Arsenal.
“If you don’t gather points there, you don’t know what the others do. The Premier League can surprise you.
“There are 12 points difference to fourth place, which is Tottenham.
“We have to work hard and be very concentrated and gather our points to step up.
“That’s why it was a pity that in the 86th minute we got this draw against West Brom, which would’ve helped us a lot.” The Chelsea interim manager says the uncertainty — including over who will replace Mourinho this summer, plus the likely lack of Champions League football — makes transfer business difficult this month.
Asked if everything is on hold, the Dutchman said: “I think so. That’s the reality of Chelsea nowadays.”
Striker has been a position of focus in transfer speculation regarding Chelsea, with back-up for Diego Costa lacking. Radamel Falcao (thigh) remains out, but when Loic Remy is fit, Chelsea have no concerns, Hiddink says: “As long as this is happening (and Remy is fit), we are not very active in doing other things.”
Costa was one of the main protagonists of a feisty 2-2 draw with West Brom on Wednesday and hit the tunnel in frustration as he left the field. Hiddink insisted there was no damage.
He said: “I did a lot of things before I got into management. I was a plumber and a builder and I checked it out the day after. I didn’t see anything.
“It was an expression of frustration, of not winning. No big deal.”
Hiddink felt Claudio Yacob should have been sent off for two yellow cards and was so annoyed with the performance of referee Anthony Taylor, he expressed his concerns to fourth official Jon Moss. He was taken aback by the reply.
“I told him: ‘This is one of the worst referees of the Premier League I have experienced,”’ said Hiddink, who had a prior caretaker spell at Chelsea in 2009.
“He said to me ‘you haven’t seen me yet’, which was a beautiful remark I think.”
Yesterday, both sides were charged by the FA for failing to control their players.
Everton beat 3-1 back in October, but Roberto Martinez, however, is still wary today.
“Remember that they won the Premier League last season and that wasn’t long ago,” said Martinez. “So the quality is there and they have players that in one second can produce a moment of magic.”