The point in Tel Aviv lifted spirits after a disappointing World Cup qualifying campaign and the duo are hopeful of taking the confidence into their European Championship challenge.
"It was important for us to finish the group on high," Davis said. "We had spoken about that before the game because there has been a lot of work put into the campaign with little reward.
"We've been able to compete in each and every game but we haven't really had the results to show that.
"This gives us something to build on for the future but I thought this time we got a decent result back."
Baird insists the point, salvaged with a goal from his captain 18 minutes from time, was the least the Irish deserved from the match.
"I thought we were fantastic against Israel throughout the game," Baird said.
"We played some very good football and got a result to be proud of. We just passed the ball with a bit of confidence and belief.
"We know we have the players who can do that, so if we can continue to do that through the next campaign I think we have great chance of qualifying."