Roberto Martínez famously outwitted Manchester City in the FA Cup final last season, but believes the side now managed by Manuel Pellegrini has grown stronger since then, despite decidedly mixed results this season.

Everton pre-Martínez have an exceptional record in recent years against City – six wins and only one defeat in the last eight meetings – though the former Wigan manager refuses to see the Mancunians, who play host to Everton on Saturday, as anything other than title contenders. "Technically, tactically and physically you need to be perfect when you face Manchester City," he said. "Fernandinho, Navas and Negredo have improved the squad, so from where they were to where they are now has been a step up. We will have to be at our very best to preserve our unbeaten record at the Etihad. Everyone will go into the game feeling they are playing a real title challenger, and that's changed from a few years back."

City hardly looked exceptional when being taken apart by Bayern Munich on Wednesday or letting a 2-1 lead slip at Aston Villa last Saturday, but Martínez believes their underlying form is better than their results suggest. "Bayern Munich have moved on to a new level, I don't think many teams could have lived with them on Wednesday," he said. "And having watched the Villa game, I felt City were a bit unlucky. They were pegged back by a goal that was offside then a super strike from a free‑kick.

"Sometimes that can happen, but I watched the performances against Cardiff and Villa and if I'm honest, at half-time if you told me they would lose either match I'd never have believed you. I don't think City played badly in either game. Football can be very harsh and I don't think the results reflect the start this City side has made. Their results are one thing and the performances are another. They have been very consistent but have conceded goals that are rare, in that you won't often see them conceded. If they perform that game at Villa Park 10 times, they will win it nine times, believe me."

Martínez accepts that the FA Cup final has no relevance now, apart from the necessity of reminding his players that they will need to concentrate for the whole 90 minutes. "A final is a final," he said. "You can prepare in a different way and this game will not be like that, but we'll have to be perfect tactically. Unless you get an advantage tactically you'll never be able to compete against the top four, that's the nature of the game. Villa found a way to outnumber Manchester City for a very specific three or four plays and it worked in their favour. You need to get your game right against City but most important you must still be able to be yourself.

"Sometimes you get too carried away thinking about the threat of the opposition and you nullify yourself. We have to realise we have to be as good as we can and then maybe we can compete against them."

Gareth Barry will be absent for the game against his parent club, and Kevin Mirallas is a doubt with an ankle injury, but Martínez sees no reason why 19-year-old Ross Barkley cannot continue his run in the first team. "Ross doesn't need a rest, he's full of energy," he said. "He can't get enough games at the moment. He is only a young man but he was been at the club a long time waiting for this opportunity. He is part of the reason we have made such a good start to the season, but as I keep reminding the players, we could have done better. It's great to have three wins in a row, but before that there were three draws in a row. Games where we played well and could have won. That cost us six points. Of course we are happy to be in the top four, but if you look at it overall, we could be higher still."