The 2011 and 2012 Bundesliga champions ended 2013 in fourth position, 12 points adrift of legue leaders Bayern Munich, who also have a game in hand.
They are only two points clear of Wolfsburg and Weidenfeller admitted that "nobody wants to see us in fourth place."
The Germany goalkeeper plans to do something about that in the second half of the season.
"Of course we can still win a title," he said from the Westphalian club's winter training camp in La Manga, Spain.
"We've just got to make sure we continue to do our homework. We have been rightly criticised for the 20 goals we've conceded so far, but we had not really settled as a team.
"Now we will try to give it a go again, even though that is getting harder by the year with other clubs strengthening."
As well as trying to close the gap on Bayern at the top of the Bundesliga, Dortmund have their sights set on winning the Champions League, where they face Zenit St Petersburg in the last 16, and the DFB-Pokal, where they meet Eintracht Frankfurt in the quarter-finals next month.