A shoot-off was required in Sunday’s skeet final after Great Britain’s Rutter and Chile’s Francisca Crovetto tied on 55 shots from 60 targets.
The pair still could not be split after three shoot-off rounds but Rutter was then adjudged to have missed a shot which replays appeared to show she hit.
Rutter, who gave birth to her first child just three months ago, contested the call but the judges did not overturn the decision and could not check on a video assistant system.
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That meant Rutter was given the skeet shooting silver medal and Chilean star Crovetto was handed a controversial gold in Paris.
‘I truly do believe I did hit that target,’ Rutter said on Good Morning Britain.
‘I definitely saw something come off it and the fact everyone at home has managed to see something too…
‘But that is sport for you. This doesn’t just happen in our sport, there’s so many sports where you see controversial decisions.
‘Even in the final it wasn’t just myself, some of the other athletes felt they hit targets but we didn’t have the footage to check so it was purely based on the ref’s decision.
‘We have had VAR systems in place at previous competitions so I’m not quite sure why we didn’t have it at the Games.
‘At the end of the day I am so pleased to come away with a medal of any colour. I can’t let that split decision and that moment take away from all the hard work I’ve put in.’
After the officials declared Crovetto the Olympic champion, BBC commentator Rory McAllister said it was a ‘moment of controversy that will be talked about for days and weeks to come’.
‘A moment of history for Francisca Crovetto Chadid and Chile but a moment of controversy that will be talked about for days and weeks to come,’ he said.
‘On the slow motion replay we saw the clay had been hit on the right hand side by Amber Rutter, which is a hit, you don’t have to hit them in the middle. But what a moment for Francisca Crovetto Chadid.’
Several fans said Rutter had been ‘robbed’ of gold in the French capital but the 26-year-old was just happy to clinch a medal after having to miss Tokyo 2020 due to a positive coronavirus test.
‘It is just a dream,’ she told BBC Sport immediately after the skeet shooting final. ‘The fact that I’m able to be a mum and come away with a medal for my country, I am on top of the world right now.
‘The fact that I am able to be here, I believe everything happens for a reason. It really was to prove a point and come back here and really chase down those medals.
‘The fact that I am here now, Tommy with me and with an Olympic medal, I don’t know how it gets much better than this.’
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