Liverpool travel to Old Trafford on Saturday before hosting Middlesbrough on Sunday, travelling to St Andrews to play Birmingham and then ending the season against Newcastle at Anfield.
It will be a difficult task to win all four games but Riise says it is what the Reds must aim for to have a realistic chance of competing in next season's Champions League.
Riise said: "There aren't many games left now and every point counts in the race for fourth place. We haven't got an easy run-in and we know we'll have to play well to stay where we want to be. Manchester United away is probably the most difficult fixture you can get in the Premiership. Nobody expects us to win on Saturday, so maybe that will work in our favour. We'll certainly be going there to get the right result.
"It's very close in the battle for fourth and I think it's going to stay close until the last game of the season. We have to keep the position we're in at the moment but we know it is going to be difficult because we have some very hard games left to play. If we don't make it then we don't make it, but I'm confident we will.
"We can't keep slipping up like we have been doing of late and relying on other teams to drop points to ensure we stay fourth. We have to start putting some wins together.
With four games to go we have to try and get 12 points and then see if it's good enough for us to stay fourth.
"I think we'll probably need four wins. If not four wins then certainly three and a draw. We definitely can't afford any more defeats. We know we still have our biggest rivals for fourthplace still to play at Anfield so that could be a massive match for us. We may need help from other teams as well, but all we can do is win our own games and then see what happens."