Fenlon saw his side lose 1-0 to Edinburgh rivals Hearts at Tynecastle and they lost their previous Scottish Premiership match with Motherwell.
Hibs were also dumped out of the Europa League qualifiers 9-0 on aggregate by Malmo but Fenlon insists they will improve.
"I've got no problem with people looking at my position, no problem at all," he said.
"I'm the manager of the club and I will continue to do that.
"We've lost two games 1-0 in the league and Europe was really disappointing.
"In both league games there was very little in them and I don't think we're too far away from getting a result. I'm very happy with the squad we have.
"We need one result, footballers live confidence-wise and a result on the board helps, it breeds confidence.
"There has been very little in the games we played and with a break of the ball, we could have got a result."