"He has played at the highest level, he knows the game inside out, and he will become a better manager for the experience he is gaining.
"Obviously the club is going through a tough period at the moment but we all hope and believe that Gareth will come through it.
"But then you can look around the Premier League and see that it's not easy for any manager.
"Look at Sam Allardyce. He's a very experienced manager but he is finding it difficult to get results at Newcastle. What you do is keep smiling, work hard and do everything you can to turn things around."
Fans have pointed out that this is only Southgate's second season at the helm, and his first relegation battle.
But Crosby insists there is enough know-how around the manager to help him deal with the dilemma.
Crosby said: "Of course Gareth lacks experience in the role. That's because of the length of time he has been doing the job. But he is not lacking in experience around him.
"I've been in a game for a long time, and so has Steve Harrison, and we've both been managers.
"There's a lot of experience among the coaching staff and Gareth has the benefit of that every day.
"In any case, the only way to get experience is by doing the job and Gareth knows what he has to do."