Ola Toivonen's spot-kick cancelled out Aleksandr Kokorin's first-half opener for Russia, while Sebastian Larsson had his penalty saved shortly after the home side - without Zlatan Ibrahimovic - had fallen behind in Group G action.
After receiving a sucker-punch early at Friends Arena, Hamren was left to rue low energy levels in the second half as Sweden played out their second consecutive draw.
"We started very well and their goal felt like a punch in the stomach," said Hamren.
"I'm proud that we could come back, even if we missed the penalty.
"But in the last 20 minutes the players lacked energy. For example Mikael Antonsson wanted to be substituted but we gave him some bananas and energy and he could continue.
"[Russia] had more days together where they could rest and practise before this match.
"I think that showed at the end when we were very tired. Ola Toivonen won't be playing on Sunday unfortunately."
Despite Sweden sitting fourth in the standings, they are only two points adrift of Montenegro, Russia and Austria, who are all locked on four points.
"I understand it's better to win one and lose one compared with having two points, but on the other hand our opponents didn't win either," the 57-year-old said.
"The fact that Austria beat Moldova and Montenegro drew with Liechtenstein shows there are no easy games at all."
