After an early scare when Lucas Ocampos missed an open goal for Monaco, the Portuguese side enjoyed a measure of control in the second half but were denied by a fine showing from home goalkeeper Danijel Subasic.
Monaco shot-stopper Subasic pulled off a string of saves to maintain parity and Benfica were forced to settle for a point - their first of this season's competition - after defender Lisandro Lopez was dismissed for a poor tackle on Joao Moutinho in the 76th minute.
Jesus was frustrated by the side's inability to beat Subasic but remains hopeful they can progress from Group C.
"Danijel Subasic was the man of the match," Jesus said.
"During the first 15 minutes we had problems. Then it was balanced and I think we deserved to win.
"The best goalscoring opportunities fell to us. Naturally after Lisandro was sent off Monaco came with everything against us, but they never caused us any real problems, even though we were not able to go forward so often.
"The next match, at home to Monaco [in two weeks' time], will be decisive. If we win, everything will be wide open."
