The new Sunderland boss tasted defeat in his first game in charge, going down 2-1 to Aston Villa to leave the Black Cats rooted to the foot of the Championship.
Sunderland fell behind to Albert Adomah’s tenth minute opener before Joshua Onomah doubled their lead with a deflected effort four minutes into the second half.
Lewis Grabban pulled one back with 20 minutes to go, his tenth of the season but it wasn’t enough to spark a comeback.
Coleman, who had only overseen two short training sessions and was without 10 first team players, admitted it was tough for his players but only they can drag themselves out of relegation trouble.
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Speaking after the defeat at Villa, Coleman said: “I think the doom and gloom at our place at the minute, bottom of the league, ten first team players unavailable, I think coming to Villa, one of the toughest games we will get, we did okay considering.
“We worked with the players for just 20 or 30 minutes. They played Saturday, had a session on Monday, so it’s very tough for them. We are out of options if we lose one or two more players. Hopefully we will have one or two back for the weekend.
“I thought it was a foul on Adam Matthews in the build-up to their first, if he doesn’t get out the way he will get nailed there and there was a deflection for the second but there are no excuses. We are bottom of the league.
“Sometimes that is what happens when you are down there, bad news after bad news and if you are not careful you get into a rut. It is only us that will get out of it - by hook or by crook.
“We have to drag ourselves through it and get a result and start marching forward. Overall, they had a go. At 2-0 down at Villa Park they could have melted but they didn’t.
“I am not too despondent with them.”
Experienced Coleman, who resigned from his post as Wales manager on Friday to take charge at the Stadium of Light, said what the players must not do is feel sorry for themselves.
Sunderland travel to third-bottom Burton Albion on Saturday in desperate need of only their second league win of the season.
He added: “They can’t feel sorry for themselves, never do that. In these moments this is where team spirit comes from, it’s where you start to build it.
“That is what we have to do. We are definitely in a fight, there is only us who can fight it.
“I don’t want anybody to feel sorry for me or the players.
“It is us that will get out of this. You keep going, keep preparing as hard as you can and you have to turn your luck around.
“We will do that.”
Coleman said he didn’t set the side out to be defensive and wanted Sunderland to have a go at Villa, with his side enjoying the lions share of possession.
“What I didn’t want to do was come here and try to be defensive for 90 minutes. In the past I have learned from that. I think we tried to play football, we just had to be cuter in certain areas of the pitch.”