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Parker saw his side consigned to the drop with three games of the season still left to play following Monday night’s 2-0 defeat to Burnley.
It confirmed a fate that has seemed inevitable for some time, with the Cottagers entrenched in a relegation battle ever since they began the season with four successive defeats.
Speaking on Sky Sports’ Monday Night Football, Parker said: “I’m really disappointed, hurt, gutted and while there’s been this looming over us for some time, we’ve been in and around it and flirted with it for a long time, there are no words at this moment in time I can put together other than I’m gutted we’ve not managed to be successful this year.
“Success would’ve been staying in this division and we’ve not managed that.
“[Our season was] probably summed up in that game, to be honest with you. Between both boxes we’ve had our moments and looked a good side but where we’ve fallen short is other side of that. Defensively, the goals are poor goals. And then we get the ball in the right areas but in clinical moments you need those details. We’ve fallen a little bit short.
“We’ve had progression, had moments where we’ve improved but we’ve fallen short at this level, there’s no denying that.”
It is the second time in a row that Fulham have lasted just one season in the top flight before being relegated.
Parker led them back up at the first time of asking with playoff final success last season, but the 40-year-old says stability is now key to taking the club forward after four yo-yo seasons.
“The rollercoaster of that and the highs and lows is not something you want,” Parker added.
“We need to try and get off this rollercoaster at this present time that we’re on.
“I’ve been committed since I came here, that’s always been the case. What’s key for me is that we sit down and analyse, learn and we’re brave enough to put our hands up and realise where we’ve gone wrong and not go through the same cycle. We need to break that cycle.
“I don’t want to come into this league for a season and get relegated. I want to stay in this league and see the club move forward.”