The Merseyside outfit posted two successive 2-2 draws in tough away fixtures against Arsenal and Manchester City over the last week.
And, with the Reds not facing an away fixture against a top 10 side in their remaining 13 games, the 32-year-old believes a late climb is possible.
"We can take a lot of belief from the way we've performed against Arsenal and Manchester City," he told reporters.
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"City are a good side and to go away to the champions and get a point is a good result, but after the way we played we're disappointed not to get the win.
"We need to build on this and I'm feeling really confident about our ability to move up the table.
"We might not have got the results we wanted against the top sides but every time we have certainly matched them if not bettered them in games.
"No disrespect to the sides we've got coming up but if we keep playing like that then we can certainly put in a challenge for fourth place.
"If we perform like that we will pick up a lot of points between now and the end of the season.
"The team is looking really strong at the moment. Before the transfer window we were lacking a bit up front as Luis Suarez was almost having to do two jobs.
"But now Daniel Sturridge has come in and given us more options going forward. Daniel has done brilliantly for us so far.
"Not many sides go to Manchester City and completely dominant large parts of the game like we did. It's just disappointing that we weren't able to hang on and see the game out."