Bassey scored in normal time as Fulham drew 1-1 at Manchester United at the end of extra-time before winning the penalty shootout.
He said afterwards: "It's a privilege and an honour to be here. To come here, it is a blessing, so I'm happy.
"I like to say I'm a bit of poacher. Trying to smell where the ball would go and reacted first. Put my head on it and back of the net.
"They're a very good team with a lot of talent. We tried to take the sting out of the game and control possession.
"They had their chances and sometimes a game goes down to penalties. We had a bit of fortune in the penalties with Leno saving two.
"I am proud of every single player."
On goalkeeper Bernd Leno, he added: "He has been amazing. He has kept us in games so many times. He deserves the recognition.
"We're buzzing and we take each game as it comes.
"That's the best way to take each game. Don't get too down with the losses and don't let the wins get to your head."