Ronald Koeman has described Roberto Martínez as “a really good talker” who left him several problems to address at Everton this season.

Martínez was a guest of Sky’s Goals on Sunday programme last weekend when he claimed to have witnessed the same defensive frailties in Everton’s 6-3 defeat of Bournemouth that blighted his reign at Goodison Park. Koeman said he would reserve judgment until the end of the season on what Martínez left him but is bemused by the Belgium manager’s negative comments about an aspect of Everton’s game that has undeniably improved.

“First of all, he is a really good talker, a good communicator and all that, as you say,” the Everton manager said. “He speaks nice and like everybody he is a human being defending himself. But I think it is easy to talk after Bournemouth about the defence. That defence had three clean sheets in a row before Bournemouth [actually two in three]. And finally the numbers, the stats, it is still not the end of the season so I will wait to give my good answer.”

Everton have conceded 27 goals in 24 Premier League matches during Koeman’s first season in charge compared with 34 at the same stage of last term. They have scored three goals fewer, 40 to 43 under Martínez, but are eight points and four places better off than after 24 games of the Catalan coach’s final campaign. Koeman insists defending was not the only problem that required improvement.

The Everton manager, who in January released several players inherited from Martínez, said: “It was not only defence. I remember one or two meetings at the start of the season where I showed what we needed to change. I took clips out of last season, including good clips of the team in ball possession but also clips out of possession because in my opinion there was not always good defensive organisation when an attack broke down.

“A big part was defending set plays – 14 conceded last season was too many. Then you need to know the character of the players, the quality of the players; if you are there with them day by day you get a different idea. Also being more direct instead of a lot of ball possession back to the goalkeeper. Play the ball in the channel … There is more high pressing, trying to press your opponent and not to wait and drop back too much. That takes time and maybe you need different players to play that system. There were several aspects of football I wasn’t happy about.”

Everton travel to Middlesbrough on Saturday unbeaten in seven league games and with Ross Barkley a growing influence on the side’s recent improvement. The England international came in for severe and repeated criticism from Koeman earlier in the season, prompting the 23-year-old to ask his manager why he was being singled out.

“I spoke about this with Ross,” Koeman said. “He mentioned that it is always about him. I said: ‘OK, start to be afraid when they don’t ask about you. Then you need to be afraid. And if the manager is still criticising you as a player then it means he still believes in your qualities. If I don’t talk about you any more than that is when you need to be afraid.’ I understand it is always difficult for him. There are always a lot of comments and questions about him. We had a conversation about this.”

Koeman also defended Barkley’s pre‑goal celebration against Bournemouth last Saturday, when the midfielder raised his arms after rounding the goalkeeper, Artur Boruc, and before converting into an empty net. “I know Ross. It wasn’t disrespect to the opponent for scoring that goal. It was a moment where he felt it’s an easy one. It was funny and it wasn’t disrespectful.” The former Barcelona defender added: “I never did that. I didn’t score easy goals.”