The Jags ended their long wait for top-flight action last Friday when they played out a goalless draw with Dundee United.
But Alan Archibald's young Glasgow side remain the 6/1 second favourites to be sent straight back down - with only administration-hit Hearts and their 15-point penalty giving the bookmakers greater concern.
Scotland Under-21 cap Bannigan, however, says the Thistle youngsters are just happy to be experiencing their first taste of top-flight action and insists there are no burdens resting heavy on the Jags shoulders.
Bannigan - whose side face Ross County in Dingwall this Saturday - told Press Association Sport: "We're here to enjoy ourselves. That's the way we approached the Dundee United game. It was great to play in and was full of end-to-end stuff.
"We're all young boys out there and none of the lads who started the game has played in the top flight before, so we're here to saviour it.
"People might put pressure on us by saying we are favourites to go straight back down but that is not what we are after.
"We want to look higher up the league - we're not just focusing on staying up. We're looking at other sides who have come up and then done well in the SPL.
"Ross County is an example to follow. They got into the top six last season and that would be a dream for us if we could do the same. But there is a long way to go yet."