The quarterback leads the league in interceptions with 15, and has been sacked 16 times.
The team's head coach told reporters: "He's an individual who has always been humble. He's always been a guy quick to give credit to everybody else and because of that, he has a tremendous relationship with the players here and everyone is in support of Eli.
"He's the guy that's put us in the position that we're in. We know there's great talent there and this is something we're all going through it, not just Eli. There's some growing pains here with some different people involved and some people we didn't get from the off-season that we would have hoped.
"Right now we're careless with the football and it strikes right at my gut because that's one of the things that we preach about the most. I'm going to state that we're going to improve, we're going to be better at this and when we do, we'll start to see the checkered flag at the end of a ball game."
The Giants, who sit bottom of the NFC East with no wins in 2013, face the Minnesota Vikings on Monday.