Although Kyle scored early on in his loan spell, Hartlepool have slipped down the table to 13th place.
On Saturday, Hartlepool failed to beat strugglers Hereford United and Wilson paid the penalty by losing his job.
Chris Turner has been put in temporary charge.
Former Coventry City manager Gary Mcllister is another manager facing an uncertain future. Leeds crashed out of the FA Cup to non-league Histon and are out of the play-off places.
He has remained defiant saying to BBC Leeds: "If we're out of position in the league or unable to pass the ball four feet to each other, then it would be a crisis. "I don't think it's quite at crisis level,"