The Toffees look set to finish eighth in the Premier League, a substantial improvement from when Allardyce took over in November, but the dissenting voices remain.
Allardyce’s future remains the subject of much conjecture but the former England boss believes a disgruntled vocal minority are drowning out the contented majority.
He said: “It’s a volatile world in the Premier League. It increases as the money increases, the pressure increases, and then there’s criticism you have to accept.
“Whether the criticism is fair or not is something you can’t let affect you. It’s an entertainment game, you’re trying to capture hearts and minds, and certainly I think, particularly from a home point of view, we’ve achieved that, not just with the results but the way we’ve played and the way we’ve beaten teams.
“We’ve obviously got room for improvement and hopefully that will be a big performance tomorrow and another win.”
Saturday’s visitors Southampton could be seen as a timely reminder of what might have been for Everton, with Saints heading into the final two games of the season in the bottom three.
Unlike Allardyce, Mark Hughes has been unable to turn around his side’s fortunes since taking over from Mauricio Pellegrino in March, although victory over Bournemouth last weekend was a big boost to their hopes of avoiding the drop.
“I’m surprised to see all three in the bottom three,” said Allardyce of Southampton, Stoke and West Brom.
“I think we’re all surprised. It can happen for many reasons. Obviously Southampton had a new manager and that didn’t work so they decided to change.
“Again with Tony (Pulis) at West Brom, there was a change of manager and that unfortunately didn’t get any better for Alan (Pardew), and now at Stoke it’s the same with Paul Lambert.
“The club makes a decision because of the fall-out of the Premier League and the money and how desperate it becomes to try and stay in the division so this is why we’ve seen a record number of managers leave their posts this season, which is considerably worrying for managers in the game and considerably worrying for the LMA (League Managers’ Association).
“That’s why I think we have such a difficult game tomorrow because of the victory they had last week, it gave them a real lifeline and we’re facing a team that’s going to be fighting tooth and nail to try to get a result against us. We’ve got to try to stop that and be fair to everybody else and try and win the game.”
Allardyce is already looking ahead to next season but did not have the positive message supporters might be looking for about their potential, stating that maintaining the status quo would represent success.
He said: “We want to try to maintain that position, eighth in the league, but it all depends on recruitment in the summer, what the quality of player might be, where is he and does he want to come to Everton, can we get him through the door to make us better?
“Plans are in place, names on lists, but whether they are achievable is another matter. Our window shutting before everybody else’s and the World Cup in between makes life extremely difficult.”
Everton will be without Dominic Calvert-Lewin, who has a small stress fracture in his back, but Mason Holgate has returned to training after an ankle injury and could be in contention next weekend.
