Steve Bruce’s men were condemned to life in the Championship on Sunday when relegation rivals Newcastle secured a 2-0 over West Ham.
In order to stay up, Hull needed a win over Manchester United combined with a failure from Newcastle to do the same and both results failed to materialise for crestfallen Tigers fans.
Chester expects the feeling he and his team-mates experienced at the final whistle to stay with them for a long time and believes the squad had too much quality to be in the position they found themselves in.
“This is a moment that will probably haunt all of us for the rest of our lives,” Chester told Sky Sports.
“Everyone is bitterly disappointed. It’s a failure that we will all have to carry in our careers and for the rest of our days.
“It’s a really difficult one to take, especially when you look around our changing room. It’s a squad that shouldn’t be in this position.”
The former Manchester United player is no stranger to life in the lower leagues having had loan spells with Peterborough, Plymouth Argyle and Carlisle United earlier in his career and he is well aware of the difficulty of bouncing straight back up.
But Chester is determined to put the disappointment of this season behind him quickly and expects the team to push for promotion next season.
Chester said: “It’s a memory that will really hurt and as sad as it is I think it’s really important that you try and get over it as quickly as possible because football doesn’t stand still and I know more than anyone how difficult the Championship is.
“We have to be (ready for the fight to get Hull back up at the first time of asking). It’s going to be a difficult few weeks.
“We’re all very disappointed as professionals but football moves on really quickly and we have to do that if we are to have any chance of bouncing straight back.”