The Championship side took an early 3-0 lead but were 22-3 down by the break as Saracens - with England captain Owen Farrell back for his first club game of the campaign - predictably took control.
However, Doncaster finished strongly with deserved tries from Jack Davies and a brilliant Jack Spittle effort.
Boden said: “We competed. We matched them physically for large parts of the game.
“The main message at half-time was the dam will always burst against a side as good as that. Eventually it did and Sarries have a lot of quality.
“We had a couple of opportunities early on where we didn’t get any reward but I was proud of the players’ effort. That was outstanding for a young bunch.”
Fly-half Sam Olver and winger Kyle Evans both impressed and Boden added: “Some said has it been hard to motivate this group?
“It never is. I think some of them have a little bit loose upstairs! They love contact and the physical side of the game.
“Sam Olver is built like a butcher’s pencil but he puts his body on the line and goes for it. They’re a great group to work with.”
Evans and fellow wideman Spittle both enjoyed making breaks against a side that included other England stars such as Elliot Daly, Mako Vunipola and Maro Itoje.
“We got them some ball near the end,” said Boden.
“We started to be able to move the ball a little bit towards the end of the game. It does help when the opponents take seven or eight British Lions off the field! They are dangerous.”
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