Their European elimination, along with three RaboDirect PRO12 defeats on the bounce, has put pressure on coaching trio Michael Bradley, Neil Back and Billy McGinty.
But Dodson is adamant the club will benefit from the patient approach rather than making a rash and ill-considered decision.
"At this stage we are not making any judgments because I don't think it is helpful when there is a large part of the season to go and we have lots of focus on the Six Nations," Dodson told The Scotsman.
"Edinburgh just need to be given some time and given some space to sort things out themselves.
"We sometimes forget that this time last year Edinburgh were going into the quarter-finals of the Heineken and on to a semi. I want people to remember this is not a bad team. It does not change to a bad team overnight.
"Clearly, results wise, the coaching group have got to do something about it and so have the players to turn things around.
"The people I am most frustrated for are the fans who turn up through thick and thin and have been given a brand of rugby that has not been good enough. Everybody has to look at themselves; we have to look at ourselves off the field."
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