Lukaku was replaced by Ross Barkley in the 67th minute at Loftus Road while Kone came off for Steven Naismith shortly after Aaron Lennon had scored what proved to be Everton's winner.
"It is too early to make an assessment, Kone took a knock on the knee and we need 48 hours," Martinez told BBC Sport.
Martinez later confirmed that Kone will have tests, but insisted that Lukaku's problem is likely just cramp as a result of an accumulation of games.
On a day when Everton all-but ended any lingering relegation fears, they were still made to work hard for their victory. QPR's Eduardo Vargas cancelled out Seamus Coleman's superb opener, before Junior Hoilett and Adel Taarabt both rattled the crossbar for the hosts in the second period.
Lennon's first Everton goal made it back-to-back league wins for the visitors, giving them a nine-point gap over the bottom three with eight games remaining.
The Merseysiders showed far more defensive solidarity than in their 5-2 UEFA Europa League defeat at Dynamo Kiev that saw them exit 6-4 on aggregate during the week.
And Martinez is hopeful they can now use the result as a springboard for a strong end to the campaign.
"That was an outstanding performance in terms of greed and the personality we needed to adapt to that type of game," he added.
"QPR have been unfortunate at home this season, have created chances and the result could have gone either way. We defended very well and scored two outstanding goals.
"The desire and application we showed gives me more satisfaction than any other victory. Now we have to make sure this performance is an incredible platform for the rest of the reason. We need to climb the table as high as we can.
"The back four were excellent, especially Phil Jagielka. It was the most impressive performance by a captain when it was most needed."
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