The newly-promoted outfit took a point from their first Premier League game since 2012, but they needed to come from behind on two separate occasions, while Everton were forced to play more than half of the match with 10 men following Phil Jagielka's sending-off.
Jimenez marked his competitive debut for the club with their second goal to earn the point, but the Mexican international believes that his side deserved more.
"I'm happy for the goal. And a little bit sad because of the result as we deserved more. But that's football. One point in the first game is good," he told BT Sport.