The result meant that Wales will not be competing at Russian Federation 2018 having failed to secure automatic qualification or a playoff spot.
Wales players decided they needed to approach Coleman, and tell him of their wish for him to stay.
Wales reaching the Euro 2016 semi-finals was an achievement well beyond expectations but there is a feeling that, with Gareth Bale and emerging young players, the side could also do well at Euro 2020. "I'll take some time to let the dust settle and then I'm sure we'll have a sit down and have a chat and we'll take it from there".
"If the powers that be can give him a really good contract and make him stay he can carry on being the greatest Welsh manager of all time".
"There's a chance I can and a chance I won't", Coleman said when asked if it was possible he could continue in a job he has held since January 2012.
"The gaffer has been great for us and I've loved every second of working with him and we'll see what happens". But right now, I'm thinking about the experience. I think he will be lined up for a big job, if that is what he wants. "It won't be easy but Chris is the man who can keep us focused and positive and show us how to get the results we need".
"It's six years I've been in charge, or coming up to it at Christmas, and I can't say right now about my future because I'm not thinking about it". There'll be a conversation in due course, there's a friendly next month. I'll go back to my family and take a bit of time. "We will wait to see if he feels if he can take this team further".
"The whole nation will be mourning and disappointed because, again, that elusive World Cup has passed us by", Coleman added.
"We've all had disappointments in football before and you get a lot more lows than highs".