The Edinburgh side have drew with Celtic on Saturday to extend a promising run of form in which they have lost just once in eight matches.
Hibs' next two matches come against Aberdeen and Hearts and Fenlon is keen to that his players do not lose their nerve. If Aberdeen are overcome at home on Saturday then the Leith club will ascend to fourth place in the SPFL Premiership.
"It's a great period for the supporters," said Fenlon. "We have Aberdeen then Hearts coming in, we had Celtic at the weekend so it is all positive at the moment. Aberdeen are a good side and they have real attacking threats in there. Again we'll have to look at it and see what game plan we come up with."