Cook, who has won medals at the previous two Olympic Games, discovered on Tuesday she would not be part of this year’s team of 12.
The talented rider, 45, secured team and individual bronze eight years ago in Beijing before collecting a team silver at London 2012.
Speaking on not gaining a place in the team for Rio, Cook said: “It’s very disappointing. I’ve felt good over the past few months and was hoping to get a place in the team.
“The sole focus for me has been on trying to make sure I got a place in this squad but I haven’t been able to do that.
“It’s all about opinion and, unfortunately, for me I haven’t been included this time around.
“After winning medals at the previous two Olympics, I was hoping to add to that tally this time but that won’t be the case now.”
As well as Cook, another 2012 team member – Zara Tindall – has also failed to make this year’s squad. Gemma Tattersall has been handed an Olympic debut.
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