Goals from Gylfi Sigurdsson, Oumar Niasse and youngster Tom Davies helped the Toffees to a 3-1 victory over Crystal Palace in front of their own fans this afternoon, a result that saw them move onto 34 points with 11 games remaining.
Of that points tally, 26 have been earned at Goodison Park - whereas away from home, Everton are ranked 17th in the league with just one win to their credit all season.
"We have to look at our own record and that is where the mainstay of our season lies," Allardyce told Match of the Day. "In the eight home games I have been here, we have picked up 17 points and conceded just four goals, we are getting it right, entertaining the fans and getting the result. The unfortunate away form is causing us the problems.
"Goodison Park has always been a strong place to play, the supporters get behind you. Away from home it has been a longstanding problem. It is something we have to try and turn around. Now we can relax and enjoy the result. We got 3-0 up and the pressure was off. Even when they scored their penalty, we were not under too much pressure. We will do some sunshine training now because we are not in the FA Cup.
"The Everton fans will wake up and be happy to see where we are, only two points off seventh. We are nearly safe and can get the planning done for next season, we can start penciling some things in.
"I was apprehensive today after being done 5-1 away from home (at Arsenal last week) but the players have responded magnificently. We have shown what we can do and hopefully we can improve for the rest of the season."
Next up for Allardyce's side is a trip to Watford in a fortnight.