The Reds have climbed to sixth in the Premier League after embarking on a six-game unbeaten run under caretaker manager Kenny Dalglish.
They remain eight points behind fourth-placed Tottenham but the Londoners' loss at Blackpool in midweek and Liverpool's improving form has kept hope of a late charge alive.
Kuyt said: "I think in the league this season, where so many teams are dropping points, a lot of things are possible.
"But we have to look to ourselves - we are unbeaten for a while now, let's have another three points on Sunday and then let's see where we are in five or six games.
"If we can close the gap a little bit more, who knows what is possible?
"It is always good when you see your rivals dropping points, but at the end of the day you have to bring the points in yourself.
"That is why the team was disappointed with the draw against Wigan, but now another game is coming up against West Ham and hopefully it will be another away win."
Liverpool will travel to Upton Park on Sunday fresh from securing a place in the last 16 of the Europa League last night.
Kuyt claimed the only goal of a testing and scrappy tie against Sparta Prague when he headed home with just five minutes of the second leg remaining at Anfield.
Dalglish's men will now play Portuguese side SC Braga for a place in the quarter-finals.
Holland international Kuyt, 30, said: "It was relief, but I thought we created enough chances to score a goal - we just waited too long.
"In the first half we created three good opportunities and the second half was the same, but I am very happy with another European goal. That is a great feeling.
"We worked hard to go through to the next round.
"It was a difficult game but we tried hard and created a few more chances than last week.
"But at the end of the day, it is the winning that counts."
After a dismal start to the campaign, the mood at Anfield has been transformed since Dalglish took over from Roy Hodgson seven weeks ago.
Kuyt said: "The key is to be positive, train very hard every day and try to progress.
"We are not satisfied with that many clean sheets or games unbeaten - we just want to move forward and be better and better.
"I think it looks a lot more positive than a couple of months ago."
Kuyt is also pleased results have been delivered without some key players.
Talismanic captain Steven Gerrard has missed the last three games with a groin injury but could return at West Ham.
Striker Luis Suarez has been ineligible for Europe and Glen Johnson was also absent on Thursday night with an Achilles problem.
Record £35million signing Andy Carroll is making good progress in his recovery from a thigh strain but is still unlikely to make his much-anticipated debut at Upton Park.
Kuyt added: "That is a big plus. If you saw the team playing today without Andy Carroll, Luis Suarez, Steven Gerrard or Glen Johnson - four of our best players - it is important that the others can do a job as well."
Joe Cole also played for 90 minutes on Thursday night after starting for the first time under Dalglish.
The England midfielder has made little impact since his high-profile free transfer from Chelsea last summer due to injuries, suspension and poor form.
Kuyt said: "I think Joe is getting better and better.
"His problem is that he had a couple of injuries and then it is always difficult to come back, but the manager gave him a couple of minutes the other week in Prague and I thought last night he did very well.
"He was just a bit unlucky not to get his goal, but I'm sure if we keep going like this, it will be just a matter of time."
