The Blues have endured a difficult start to 2018 following a slump in Premier League form and a series of cup exits.
Chelsea FC lost 2-1 to Arsenal in the second leg of their League Cup semi-final at The Emirates back in January.
The west London outfit lost 4-1 to La Liga giants FC Barcelona in the Champions League round of 16.
The title holders have lost four of their last six Premier League games to tumble down the Premier League table.
Chelsea FC were 2-1 winners against Leicester at the King Power Stadium after goals from Alvaro Morata and Pedro Rodriguez.
Former Blues striker Sutton believes Conte has bought himself some more time with their vital FA Cup victories.
“It was a massive win for Conte,” Sutton told BBC Radio 5 Live.
“It’s the only trophy they can win. They’re not going to get in the top four. They’ve got too much work to do.”
Chelsea FC signed England international Ross Barkley, AS Roma defender Emerson Palmieri and Arsenal striker Olivier Giroud in the January transfer window.
The Blues have won the Premier League title in two of the past three seasons under Jose Mourinho and his permanent replacement Conte.
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