The Eagles are winless in the Premier League since the start of the year but have claimed creditable points against the likes of Manchester United, Newcastle United, Brighton & Hove Albion and Liverpool in SE25.
Their next week is set to prove equally as challenging, if not more so, with three games in eight days against title-chasing pair Manchester City and Arsenal, as well as a midweek trip to Brighton.
Mitchell said of the visit of City: “I think against any big team, you’re going to have to compete your best, because if you don’t then you’re going to be in trouble against any team in the Premier League – but especially against a bigger team.
“It’s something we know and something the fans know too. I feel like there’s an extra bounce when you’re playing the bigger teams and doing well against them. The stadium’s on fire, so it just helps you get through the game either way.
“[We next face] teams who are in-form this season, so it’s definitely going to be a hard few games, but every game in the Premier League is hard, so we’ll just train hard and be prepared for them.”