Walcott proved the match-winner on the night, scoring his first two goals for the Club since his January move from the Gunners, which proved enough despite Jamie Vardy's second half penalty almost triggering a Foxes fightback.
But the 28-year-old insisted it was a combination of the team and the fans that saw the Blues home and dry, as they registered their first win in eight matches.
“The team were talking together and the crowd were behind us," he said. “It was a togetherness tonight and that is what was needed going into the weekend [against Arsenal].
“For me personally, to score my first goals at Goodison was brilliant. The home support is fantastic and to get the win for the team is the most important thing.
“It was needed tonight. We had to dig deep in wet, windy and cold conditions. But the guys did really, really well."