The reigning Premier League champions have lost three consecutive games - in different competitions - and are in seventh place in the league, 11 points behind leaders Arsenal and in danger of missing out on Champions League qualification.
Spanish stopper De Gea said the players are staying behind after training sessions to try to improve.
He told the club's official website: "We frequently stay after training to practise crossing and finishing.
"We do it especially when there are no matches in the following days and I think the extra training helps me and the other players to improve."
De Gea has teamed up with Mexican striker Javier Hernandez to try to improve each other.
He added: "We help each other - he tries to make it difficult for me and I try to make it difficult for him. We always do our best and he's a player who gives his all in training.
"He is one of the most professional players I have known over the course of my career. He is truly a great player and a good friend."
United slipped to a third successive defeat for the first time in almost 13 years when they lost 2-1 at Sunderland in the first leg of their Capital One Cup semi-final on Tuesday evening.
That loss, coupled with their FA Cup third-round exit at the hands of Swansea and the fact they face the Welsh outfit once again in the Premier League at the weekend, is a growing cause for concern for manager David Moyes and his side.