The Eagles face Manchester United at the Stadium of Light in their opening Champions League game tomorrow boasting a proud record in Europe's number one club competition.
Twice they have lifted the trophy, whilst Benfica have also been runners-up on another five occasions, including in 1968 when they were beaten by United at Wembley.
However, it is 21 years since their last appearance on the greatest stage and over the past decade they have got no further than the last eight, which in itself only happened once.
Domestic rivals Porto did win the tournament under Jose Mourinho's guidance in 2004 but since then heavyweights from Spain, England and Italy have dominated, Bayern Munich responsible for the only finalist from outside those three European heavyweight countries.
Jesus accepts the battle is becoming increasingly lop-sided.
However, he uses the presence of three Portuguese teams in the semi-finals of last season's Europa League - including Benfica, who were beaten by fellow countrymen Braga - as evidence of what can be achieved.
"Usually in the Champions League, the teams at the top are the ones who are strongest economically," said Jesus.
"Teams from Portugal have to work in a different way. We have to discover players without money.
"We have to work in order to get these top players but our results proved that we can still surprise teams."
Jesus has not completely ruled out the chances of Benfica recording a record of one win in seven attempts against United.
However, he has dismissed the possibility of last year's runners-up not finishing in the top two, meaning the battle for qualification is between three teams, Benfica, Basle and Romanian debutants Otelul Galati.
"It is going to be very close," he said.
"Manchester United are the clear favourites but I think it will be a fight to the end for the other teams."