Henderson was part of the Liverpool side beaten 1-0 at home by their bitter rivals, with the defeat leaving Jurgen Klopp's side ninth in the table - eight points off Tottenham in fourth.
If losing to United was not bad enough for the Liverpool skipper, Henderson is worried any hopes Liverpool harboured of Champions League football next season could be finished as a result.
"I am not sure if the top four has gone. At the moment we are not in it, but we have to keep on fighting," he said.
"We are getting chances, we are creating chances but we just couldn't finish them off against United for whatever reason.
"So we just have to keep going. Sometimes football is like that, sometimes you play well and get beat."
READ MORE | Klopp frustrated by wasteful Liverpool
Henderson was one Liverpool player guilty of spurning chances - notably sending a good opportunity wide of the far post in the first half.
But failure to take opportunities was only half the story as Henderson bemoaned Liverpool's continued struggles when defending set pieces.
"When the disappointment goes away and we actually analyse the performance there were a lot of good things in the game but we just couldn't take our chances and we lived to regret that later in the game," he said.
"We paid for the chances we missed and conceding from a set piece was disappointing as well."
As inconsistency continues to plague Liverpool's season, Henderson also said it was inevitable that manager Jurgen Klopp would look to make additions to his squad.
"Football teams will always look to strengthen, always look to improve, but us as players, we just have to give everything for now. All we can do now is keep going until the end of the season," he said.
"We have to keep going right until the very end and see what happens, whether you are in the mix or you are not. I really believe we have a good squad of players but [games] like today we need to be winning."