The striker scored twice on Saturday as the defending champions were held to a 2-2 draw with Watford in the Dutchman's first game since returning to Stamford Bridge as manager.
Oscar missed a late penalty to secure all three points, while, with two minutes remaining, Costa was shown a yellow card that rules him out of the trip to Old Trafford.
Hiddink admitted it is a shame he will be unable to select the former Atletico Madrid striker when he looks to be returning to form.
"He is out [on Monday], which means that we have to think how to solve that problem," Hiddink said.
"It is a pity after a good performance, we have to solve that in 48 hours."
Costa received a harsh reception from the supporters in last weekend's 3-1 win over Sunderland, and Hiddink praised his response to the criticism but denied he was responsible for the upturn in form.
"Don't overestimate the influence of managers. You try to give people focus," Hiddink continued.
"When he was booed when he was substituted [against Sunderland] his reaction was very good.
"It was a very professional reaction as it made him think: 'How should I go on?'
"He focused on what he is good at and he's very dangerous, that's important, not wasting energy where he shouldn't waste it.
"Everyone knows what he is capable of… he showed that today with two terrific goals."
