David Moyes was delighted his side were able to allay his fears with a 2-0 win over QPR on Saturday afternoon.
Goals from Darron Gibson and Victor Anichebe in either half earned a vital three points for the Blues as the league run-in picks up pace.
With six games to go, starting away to fellow European hopefuls Arsenal on Tuesday, pocketing all three points at Goodison was paramount.
And despite the visitors' lowly position and ever-increasing prospect of relegation, the Blues boss revealed he was wary heading into the fixture with Harry Redknapp's side.
"It was always going to be a game where I had fears, I've got to say," said Moyes.
"We've been playing well and picking up good results but we've not had a great record against QPR since they came up.
"I was a little worried about it. QPR are desperate for the points for different reasons to us, but overall I thought we did a professional job.
"We played some good football at times and made quite a few chances but didn't convert them all.
"I'm more than satisfied with the result."
A third clean sheet in as many home games was a welcome bonus to the result and Moyes was left to praise the professionalism of his players in their performance.
"I said to the players that the job was to get this game done," he added.
"The players have got a real resilience and toughness to them. Because of that, we keep at it and the players know what is expected.
"A clean sheet was important because we lost two goals at Tottenham but we picked up a couple of clean sheets the week before.
"It's important that you do that at this time of the year."