Simeone's side are flying high in the La Liga, with only goal difference separating themselves and Barcelona at the top of the table.
And they continued that form at the Nuevo Estadio La Victoria as a first-half penalty from Diego Costa and second-half strikes from Adrian and Raul Garcia saw them home against their Segunda Division B opponents.
"I'm very happy with the work of my team," Simeone told reporters after the match.
"There was a nice atmosphere.
"The team responded to the expectations I had. As I said, Jaén had impressive midfield players and forwards with speed.
"Obviously we knew of these strengths and I think we controlled the game."
There was a worry for the Argentinian when Cristian Rodriguez was stretchered off after 77 minutes with a leg injury, but Simeone is confident he will be fit to face Valencia this weekend.
"There has been no bad reaction so I imagine that Saturday will be fine," he added.