Saturday’s 1-0 defeat at Watford leaves the club 14th in the Championship - having taken just three points from a possible 15.
But Graham, who rejoined Boro on transfer deadline day , says the team is determined to get back to winning ways.
Danny Graham: "The Championship is a strange league and teams can go on all sorts of crazy runs.
“We’ve got to keep believing, there’s no point in giving up in football.
"I know for a fact that the boys in the dressing room certainly won’t be giving up.
“We’ve got some big characters in the team so we’ll definitely be giving it our best shot but we need to start winning games sooner rather than later.
“I got a great reception, I have a lot of friends here, but it was not the result I was looking for.
“I think it’s five games since we’ve scored.
"We’ve been defensively sound but we gifted Watford a goal with the penalty.
“We’ve got a good foundation but we just need to do it at the other end and that’s what we’re working hard to do.
“We just need a bit of luck in front of goal and I’m sure we can have a good end to the season.”
PLEASE VOTE ....
Gus Poyet insists he would take Premier League survival over cup glory despite seeing his team edge closer to a second big day at Wembley.
Gus Poyet: "Me, I would prefer to stay in the Premier League.
"Apparently to be more famous, it's better to win the cup.
"I don't want any more people knowing me, I think they know me enough, so I would prefer to stay in the Premier League.
"I am not looking for a statue, that's for sure.
"It's a personal feeling. I can't answer for anybody else, it's me. I would be devastated if we go down, so it's me.
"Now at the same time, I have to say if we win the cup, I am going to be jumping up and down and I am going to be wanting to come back here and celebrate with the fans, that's true.
"We will see, we will see what happens."
PLEASE VOTE ....
Obviously we want to win a cup AND be playing Premier League football ... but if you were put on the spot ... which would YOU choose?
PLEASE VOTE: http://www.sunderland-mad.co.uk/interactive/voting_polls.asp