Kuyt, Liverpool's top scorer last season with 15 goals, came off the bench at Anfield and struck a late winner past David de Gea to knock bitter rivals out of the FA Cup and send the Reds through to the fifth round, where they will Brighton.
Despite being an Anfield favourite, Kuyt has found game time limited under manager Kenny Dalglish, who has plumped for Luis Suarez and Andy Carroll for much of this season.
However, having bagged his first goal in Liverpool colours since the Carling Cup win over Brighton last September, Kuyt is hoping he can play a key role as the season reaches its climax.
"It was a great feeling when it [the strike against United] hit the net, especially as I haven't been scoring many," Kuyt said on the club's official website.
"Last year to score a hat-trick against United was something really special. But to score so late with the stakes so high to win us the game was maybe even better.
"I've been used to playing every game for the past 10 years of my career but it's the manager's decision and you have to respect that, especially when the manager's name is Kenny Dalglish. I have to prove myself to him on the pitch and in training.
"I've been playing more and more now since the start of the year. I've felt stronger and for me it was just a matter of time before I scored again."
Kuyt was also full of praise for much-criticised team-mate Andy Carroll, who played a key role in Kuyt's winner, flicking on the ball into the Dutchman's path.
"I thought Andy played a great game and he worked really hard," Kuyt added.
"I know how difficult it is to be alone up front but he battled throughout the game. He was important for us for both our goals.
"The header for the last goal was something I had told him. I said, 'Win the header and flick it on' and he did that perfectly."
Liverpool are back in Barclays Premier League action on Tuesday evening when they travel to Wolves.