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Efimova, who was allowed to compete after appealing against a doping ban, took silver with Tutton fourth.
"I would've preferred it to have been a completely clean Games," the 20-year-old Welsh swimmer said afterwards.
"I couldn't help who was here. I'm not happy with it, but that's how it is."
Rie Kaneto won Japan's seventh gold medal at Rio 2016 to beat Efimova into silver.
China's Jinglin Shi won bronze, just six one-hundreths of a second ahead of fourth-placed Tutton.
Her British team-mate Molly Renshaw, 20, finished sixth.
"Being fourth is a bit gutting, no matter who is in front of you," Tutton added.
"It's a great experience and I'm a bit disappointed to come fourth. I'm so close to a medal and that would have been a dream.
"But just to get into the final is a great experience that I'll take on with me for years to come."
"It was a bit gutting but it will make me tough in the long run and it just makes me more hungry for a medal so hopefully next time I'll get closer."
Efimova, who said she was tired of answering questions about her doping past, defended her right to compete at Rio.
She was banned for 16 months in 2013 after traces of an anabolic steroid were found in her system.
Earlier this year she was given a provisional ban after testing positive for meldonium, but the International Swimming Federation lifted the suspension after advice from the World Anti-Doping Agency (Wada).
The Court of Arbitration for Sport (Cas) has ruled that athletes cannot be banned from Rio on the basis that they have been previously sanctioned.
"Cas considered my appeal and I won. If someone dislikes it and has a different opinion, they can go to CAS," she explained.
"I am not for doping and I have never used it. The second case was completely not my fault. Everyone should have a second chance. When you drive and you are just issued a ticket, no-one puts you in jail."
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Earlier, Ben Proud set a British record to reach the men's 50m freestyle final.
Commonwealth champion Proud, 21, swam a time of 21.54 seconds to qualify fifth fastest for Friday's final (02:44 BST Saturday).
Find out how to get into swimming with our special guide.
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The move was announced after an urgent meeting of Ukraine's National Security and Defence Council in Kiev.
It follows weeks of unofficial action by war veterans and activists, who have been blocking roads and rail lines.
The blockade is hugely damaging to industry in the rebel-held east - but also to the wider Ukrainian economy.
On Wednesday, the council said it decided to act because of a "sharp escalation of Russia's aggression against Ukraine and the seizure of Ukrainian businesses" by the rebels in the Donetsk and Luhansk regions.
It said the decision would remain in force until the separatists handed back control of the businesses and also complied with the 2015 peace agreements signed in Minsk.
War veterans, activists and some lawmakers had for weeks demanded that all transport links with the rebels be cut, describing any business activity with the east as "trade in blood".
The veterans had also repeatedly clashed with police sent to dismantle makeshift blockade points.
The unofficial blockade has cut off vital links between industrial plants on either side of the conflict's frontline.
As a result, operations at several steel and coal plants on the separatist side have been suspended.
The blockade also puts at risk Ukraine's energy supply.
Ukraine is dependent on anthracite from the rebel-held areas, while Donetsk and Luhansk need coke produced in Ukraine's government-controlled regions.
Earlier this week, rebel leaders announced that they started shipping coal to Russia.
More than 10,000 people have died since the Russian-backed rebels seized parts of the Donetsk and the Luhansk region in April 2014, triggering clashes with Ukrainian forces.
In March 2014, Russia annexed Ukraine's southern Crimea peninsula.
Great Britain's Chloe Tutton appeared to criticise controversial swimmer Yulia Efimova's presence in Rio after the Russian finished ahead of her in the 200m breaststroke.
[NEXT_CONCEPT]
Ukraine has halted the movement of all goods in and out of areas seized by pro-Russian separatists in the east of the country.