Dave Artell's first-half strike saw Crewe leapfrog Oxford into seventh place and extend their unbeaten run to 14 games.
Davis is delighted that his side now hold their destiny in their own hands, but insists that they won't take anything for granted.
"We've given ourselves a real chance of making the play-offs with two games to go and the way we are playing I think we can beat anybody," he said. "As long as we can keep our belief and feet on the ground we can go all the way.
"They came to stop us which is great because it shows how good we are becoming. We are becoming a team that nobody wants to meet and the players deserve the credit for that.
"I was really pleased with our attitude and desire. All that mattered today were the points and on the whole I think we deserved all three of them. Now it's in our hands for the last two games but nothing is going to change in our attitude."
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