The reigning Premier League champions currently sit seventh on the table, seven points off fourth-placed Liverpool, but Fletcher is confident they can get the required results to see them into a Champions League position.
"It's all about character now no doubt about it," Fletcher told Sky Sports.
"The team has been written off, everyone has had so much to say about the situation and it's now time for the players to step up and prove people wrong and to finish the season strongly.
"It's the biggest club in the world and as soon as you are not up to a level it's like the end of the world - but every defeat is like that. We're experiencing that now and sometimes you need those moments to appreciate the success.
"The squad is definitely capable (of a top four finish this season). We have to go on a run, there's no doubt about that.
"As I keep saying let's finish the season strongly, get in the Champions League - we're still in the Champions League this season as well and our form has been fantastic - and let's carry that through to next season."
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