The Reds have moved into title contention after going on a great run of form to climb to second spot in the table, four points behind leaders Chelsea and with a game in hand over the London outfit.
Marsh insists no-one at the club is getting carried away by their fine form and claims they are taking it just one game at a time as the season draws to an exciting climax.
"We haven't achieved anything yet," Marsh told the Liverpool Echo.
"We have nine games to go and are in the Champions League places.
"It has been well documented that we started the season wanting to finish in the top four and we are in with a shout of that. Anything more than a top-four finish would be a bonus.
"We are taking each game as it comes and just trying to win every game.
"We have nine games left and are trying to get as many points as we can and see where that takes us. Our goals haven't changed since the start of the season.
"We are second with nine games to go and so are on course to get back in the Champions League. Anything better than that would be fantastic."