Martin Paterson's first-half header ended manager Michael O'Neill's long wait for a victory, and Davis feels it was no less than the home side deserved.
"We tried to make things difficult for them," the Southampton midfielder told Sky Sports.
"We worked hard tonight and it's nice to eventually get a reward for all the hard work put in.
"Russia are the top team in the group, they're a very difficult team to play against. They didn't give away many chances tonight and I thought we were outstanding, we deserved to win.
"Our performances throughout the campaign, we haven't really got the result to go alongside them but tonight we managed to do that."
Goalscorer Paterson added: "It's a great win against a very strong team.
"International football can be difficult, even at home, so we're delighted with the win."O' Neill had nothing but praise for his young side as they upset the odds in the absence of several more experienced players.
"(We did) nothing different that we haven't done in previous games, but tonight we just had 11 real players on the pitch, 13 for the lads that came on," he said.
"The work rate of the team and their quality on the ball was excellent.
"You can get carried away but it's a big result for us, no doubt about that. We were playing against a very, very strong team.
"I think we had six players on the team who've had less than 10 starts for Northern Ireland, so that gives an indication of where they are in terms of their development. They were fantastic."