The Chelsea forward, who is on loan at the Liberty Stadium, had two chances to score in the 0-0 draw at St Mary’s.
His presence caused the Saints problems all afternoon but the 19-year-old was unable to mark his competitive debut with goal, being denied with a header and a volley.
Abraham admits he should have scored his headed chance in the first-half but he is now determined to prove his worth against the Red Devils this weekend.
He told Wales Online: “I thought it was going in, when it left my head I felt I had made good contact and that it was going to be going into the net.
“Unfortunately these things do happen and I am disappointed because had we scored there we could have been coming away with a 1-0 win.
“I had another good chance when I managed to turn away from my marker in the area and I was glad to be able to show the fans some glimpses of what I can do.
“If chances like those come up again then I will be doing everything I can to make sure those chances are going in.”