"There's no need for us to be down ... We'll keep going and try our best to stay in this league as that's where I want to be, and why I signed an extension," Clayton told British media.
With their FA Cup quarter-final clash against Manchester City on March 11, Aitor Karanka's men will likely need to punch above their weight to reach the next round.
"We're in the FA Cup quarter-final so that's something to look forward to, one win away from Wembley, and we're still fighting to be in this league," Clayton added.
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The semi-finals and the final of the FA Cup are played at Wembley.
"We only need a couple of wins and the positivity will be back and we'll be flying again."
Middlesbrough travel to take on 10th-place Stoke City on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Richard Lough)
