Meanwhile, Swansea have pulled themselves four points clear of the relegation zone, though they drew last weekend against Brighton, a match that they should've been looking for three points in.
Big Sam will be reasonably happy with a 0-0 draw against Liverpool though some may argue that with some Reds players rested and minds on that Champions League game against Man City, that was as good a chance as any for Everton to have actually won the game.
'I was itching to get back because the three games plus the global break, it has been a month since I have played, ' he said. Now they need to finish strong to keep it that way, which next brings Everton to Liberty Stadium on Saturday, April 14.
"Just look at the Roma and Juventus games", said Carvalhal.
"If you look at their home record and the teams they have beaten on their own ground we were more than aware of the challenge in front of us".
There were mixed fortunes in the Everton midfield with Wayne Rooney rightfully being substituted following a poor performance but Morgan Schneiderlin fared far better. Tammy Abraham scored his first goal since October to fix the damage but could not offer much more due to a succession of poor first touches of the ball. That was Jordan Ayew, who is 5/1 for first goalscorer honours.
Everton nearly snatched a victor when Seamus Coleman struck the crossbar 15 minutes from time, but it is now only one victory in eight games for the Toffees.
Lee Probert is one of the league's more lenient referees.
'We are five points ahead of the bottom three now and this is a step forward.