Carlton Morris struck the winner on 90 minutes for the hosts.
Edwards later said: "We spoke before the game about how important it was. You can guarantee effort, try to be organised and carry out a game plan but you can't guarantee a win.
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"The character we showed, we found the result when it as really important to do so.
"I thought the second-half performance was really good. There was a belief there. The subs made an impact. I'm really pleased.
"I feel we've had one and a half really difficult games against Bournemouth - the Tom (Lockyer) situation first time and then we were 3-0 up and lost 4-3. It's a nice feeling to turn that round and grind that win."
On his plans tonight, he added: "I'll probably start losing sleep about Man City and trying to think about how to stop them."