The Cottagers were left frustrated after they had to settle for a share of the spoils against the Toffees, leaving them without a win in five competitive matches.
Unfortunately for Marco Silva, Diop and Jimenez were unable to come through the game unscathed, giving the Fulham boss a couple of injury concerns ahead of Saturday's meeting with Burnley.
Jimenez was replaced at half time by Brazilian forward Rodrigo Muniz, before Diop made way for the experienced Tim Ream in the 75th minute.
Speaking in his post-match press conference, Silva told reporters: "Both came off with some hamstring issues there".
"Let's see how they are going to be in the next hours. They are going to be assessed by the medical department and let's see how they're going to be.
"When you have some issues in the hamstring, it's not a good sign. When you play three games in seven days, such intense games and all that stuff, you have always a risk there.
"In some moments it's possible for us to rotate, but it's not been easy to rotate some players, too, and we have this type of risk that we have to take."
Silva has already had to deal with one injury setback in recent days after Harry Wilson was ruled out for two to three weeks with a shoulder problem.
Meanwhile, off the pitch, Silva has admitted that he does not expect the club to make any signings before Thursday's transfer deadline.
"I'm not expecting many things until the end of the market," the Fulham boss added. "If it was possible to do something we should have done it at the beginning of the market with the semi-finals and the FA Cup. The board is trying to do their best."
Having picked up 25 points from 22 matches, the West London club are currently sitting in 12th position in the Premier League table.