The Brazilian's shot from the edge of the area took a heavy deflection off David Affengruber and wrong-footed the Fulham goalkeeper, cancelling out Lisandro Martínez's 63rd-minute own goal. Cunha had also seen an earlier effort clip the woodwork, while Bruno Fernandes struck a post from his cutback.
Speaking to BBC Match of the Day, Cunha said:
“I think we created a lot. Fulham played well also. We got our chances, if we finish them we can finish game with three points.
“Bernd Leno is always a good goalkeeper, today he was unbelievable. We have to congratulate him but also improve.
“To beat Leno today we needed a bit of luck, and I got that luck to score the goal. Maybe if it doesn't touch anyone it doesn't go in.”
The point leaves United with one win, two draws and two defeats from five league games, after a home defeat to Manchester City and a Carabao Cup exit against Brighton earlier in the week. Cunha addressed the pressure that comes with it:
“It's only the beginning, to play for this shirt there is a lot of noise around. We stay very strong, we believe in our group and manager. We showed everyone how we did it last season. The only thing we can do is work more.
“When I don't win games I feel anxious to play the next one to win, the only way to improve is to train and play.”
Manchester United finished third last season after Michael Carrick took over in January. In a separate interview with Sky Sports, Cunha was more critical of how the afternoon began:
“It's frustrating for us, I feel in the beginning we put the plan in, we created some chances. We didn't score, unlucky, they scored in one action. It's hard to explain.
“After the goal, we played much better with a lot of enthusiasm and character. This needs to be from the start.”
Asked about starting slowly, he said:
“It's hard to explain, I feel after the first half we always get a lot of chances and create, play well.
“In the beginning of the second half they put in more energy than us and we cannot accept this. We always play better after conceding goal, and it cannot be like this.
“I don't think today was about final decisions, we were a bit unlucky, I hit the post, and Bruno hit the post. We need to create more and hope the luck comes and we score. We need to improve in every single position.”
Manchester United are back in action at home to Tottenham Hotspur on 10 October, three days before a Champions League trip to Atlético Madrid.