AFTER reports that Vern Cotter, their head coach, might be head-hunted by his native New Zealand, Scotland's players have made it clear they want him to stay and finish the job he has started with their side. After a period of instability, he has settled the team and, as they head home after winning both Tests in Japan, it is clear he still has the backing of his players.

"He is massively important," said Stuart Hogg, the full back. "He's a great guy to work under. He just wants the best for each individual and for us as a team and a nation. It's great to work with him – I'm already looking forward to being back for the autumn tests."

Cotter's contract with the SRU is up in less than a year, but there are reports in New Zealand that he is on a shortlist being drawn up by the union down-under for who will replace Steve Hansen when he leaves the All Blacks at the end of the 2019 World Cup.

Cotter himself was refusing to comment, though he says he is willing to talk to the Scots if they want to extend his deal beyond its expiry date next summer. "I am just waiting to hear from them," he said. "I am just doing my job. If they want me to stay I guess I will have a talk with them.

"I could have a talk and we sit down and they tell me they don’t want me to stay. We will sit down and discuss what is best for Scottish rugby."

If he is to be seriously in the running for the All Blacks, however, he is going to have to get Scotland playing a lot better than they did on this tour. Though they won both Tests, the first by 13 points, the second by only five without scoring a try, it was more a testament to mental resilience than rugby skills.

"It wasn't a complete performance by any means but at the end of the day were walking away with two wins," Hogg pointed out. "The conditions were tricky. It was really humid, the ball was slippy but we need to adapt to things like that more quickly. So i

"It wasn't a complete performance but we showed a lot of guts and determination to come back to get the win. All credit to the boys, it's a happy changing room.

"We believe we’re a lot better than that; we know we’re a lot better than that. We got the win and we’re happy with that and will enjoy our time off, but Australia are next up for Scotland and that's a massive test for us.

"We believe we’re a lot better than that. We know we’re a lot better than that. We got the win and we’re happy with that, but Australia are next up for Scotland and that's a massive test for us."

It is going to be a memorable summer for Hogg, who is one of four Scotland caps getting married during the close season – Pat MacArthur, Tommy Seymour and Peter Horne are the others – but when it comes to making it memorable on the rugby front, they all know the performance against Japan will not be good enough when it comes to the bigger tests to come.

Cotter knows it too, pronouncing himself satisfied with the results but less happy about the way they were achieved. "It was good to spend more time together and it was different, another experience. It was difficult. The heat, the difference in food, the jet lag.

"We came over here and we wanted to win both Tests. We are happy we did that. Some of the content was very good. We needed to be tough mentally and we have got victories. That is what the players want to play for. We did it hard, there is no two ways about that, but we got there.

"We knew the first half was going to be tough and I thought they had the edge on us in contact. They were very physical and we were a little bit sluggish due to the conditions and the speed they were playing at.

"We need to keep getting better and better and developing our game. that is why we spent time together. I am looking forward to November [when they play Australia, Argentina and Georgia], that will be the toughest autumn series I have had."

The problem with this game was that Cotter's men could not build their attacks with any consistency as unforced errors were allowed to undermine their attacking efforts. Fortunately their defence was spot on most of the time, giving away only one score that should be in the running for the try of the season after a 90-metre attack ended with Kaito Shigeno, the scrum half, crossing under the posts.

What they were masters of was forcing penalties and seven successful kicks, three from Henry Pyrgos and four from Greig Laidlaw, who replaced him, turned out to be enough.

Japan: Try: Shigeno (19mins). Con: Tamura. Pens: Tamura 3 (6, 29, 48)

Scotland: Pens: Pyrgos 3 (2mins, 15, 25), Laidlaw 4 (52, 60, 68, 77) Scoring sequence (Japan first): 0-3, 3-3, 3-6, 10-6, 10-9, 13-9 (half time), 16-9, 16-12, 16-15, 16-18, 16-21.

Japan: R Matsuda (P Paea, 77); M Sa'u, T Bennetts (K Ono, 55), H Tatekawa, Y Sasakura; Y Tamura, K Shigeno (K Uchida, 62); K Inagaki, S Horie (T Kizu, 60), K Hatakeyama (S Kakinaga, 55), H Ono (K Yatabe, 65), N Kotaki, H Tui (R Holani, 60), S Kin, A Mafi.

Scotland: S Hogg (Glasgow Warriors); T Seymour (Glasgow Warriors), M Scott (Gloucester), P Horne (Glasgow Warriors) S Maitland (Saracens, S Lamont, Glasgow Warriors, 79); R Jackson (Harlequins, H Jones, Stormers, 57), H Pyrgos (C) (Glasgow Warriors, G Laidlaw, Gloucester, 48); R Sutherland (Edinburgh, G Reid, Glasgow Warriors, 41), S McInally (Edinburgh, F Brown, Glasgow Warriors, 41), M Low (Exeter, W Nel, Edinburgh, 41), R Gray (Toulouse), J Gray (Glasgow Warriors), J Strauss (Glasgow Warriors), J Barclay (Scarlets, T Swinson, Glasgow Warriors, 68), R Wilson (Glasgow Warriors, J Hardie, Edinburgh, 44).

Referee: M Mitrea (Italy)

Attendance: 33,073