The Swans become the first Welsh club to play in the Premier League when they face Manchester City at the Etihad Stadium on Monday.
The south Wales club have been seen by many as one of the favourites for relegation since they secured promotion to the top flight with a 4-2 play-off final win over Reading in May.
Rodger that: Swans boss Rodgers would take 17th place if offered
A trip to face Roberto Mancini's FA Cup holders is about as tough a start as Rodgers and company could have been given and it highlights the task facing Swansea.
Rodgers secured club-record signing Danny Graham for a ?3.5million fee during the summer, but City on the other hand have just parted with ?38m for their record acquisition Sergio Aguero.
Rodgers acknowledges the club do not have the resources of their Premier League rivals but believes they can cause problems, starting with the visit to Manchester.
He said: 'We understand the scale of the task, not only on Monday but throughout the season, but we will look at it and take every positive we can from our own game and hopefully cause problems to the other teams.
'We are competing against Manchester City on Monday night - a club who have trillions of pounds. Not just millions or billions - trillions. But that won't stop us fighting.
A world away: Manchester City spent ?38m on Sergio Aguero
'I would absolutely take 17th if we were given that now, but there is no reason we can't do a lot better.
'The reality is we want to finish as high as we can. I won't be telling the players to finish 17th because I believe we can be higher than that.
'Of course, the miracle would be to stay in the league and try to make this club a sustainable one.
'It's a massive achievement to arrive here but it is a bigger one to stay here.
'We know it will be a roller-coaster ride but I'm excited about the challenge.'
While he is now established at Swansea, Rodgers was linked to a role in Mancini's backroom staff at City before taking over at the Liberty Stadium last summer.
And the 38-year-old is not critical of the club's big-spending approach, believing that the Citizens are also attempting to build for the long term.
'It will be a massive challenge, if you look at Manchester City it is a club that is really moving forward,' he said.
'They are looking, I suppose, to be one of the superpowers of European football with the finances that they have, but I also think they are trying to build something there and it's not just a case of totally throwing loads of money at it.
'They have got some great people behind the scenes like (football administrator) Brian Marwood and obviously the manager has been brought in to try and influence their progress.
'But for us we will do what we have always done. We have big respect for every opponent that we play, but the idea is always to focus on our own strengths and hopefully cause Manchester City problems.'
And Rodgers hopes, however the season turns out, that his side can do Welsh football proud.
He said: 'We are very honoured to be the first Welsh club to get into the Premier League and we hope we can do the badge, the club and the country as a whole very proud. We will fight for our life to try and compete in the league.'
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