Andy Murray can see summit despite latest fall on climb

Down and out: But Murray is taking positives from his defeat by Djokovic (EPA)

Andy Murray believes he can become world No 1 despite falling just short of a remarkable Australian Open semi-final victory over Novak Djokovic, the man who holds that ranking and three Grand Slam titles.

While Murray's critics – they must be reducing in number given the way he fought over five gruelling sets with Djokovic – will argue that having reached the Australian final in successive years, this result is a step back,the manner of his performance while losing 6-3 3-6 6-7 6-1 7-5 suggests otherwise.

Instead of meekly falling in straight sets as he did in those two final appearances in Melbourne against Roger Federer and Djokovic, Murray showed he has improved both his technical and mental abilities and now wants his new coach, Ivan Lendl, to take him to the very pinnacle of the sport – and a first Slam title.

Murray, who will decide shortly on his fitness for Britain's Davis Cup tie with the Slovak Republic in Glasgow starting on 10 February, said: "You're always going to have people that doubt me and say, 'He's not that good' and 'He's not as good as them'. I am aware that I still need to prove some things and win a match like this. It was so close.

"But I need to make that last little jump and I am much closer than I was at this stage last year. I don't know how much Novak can keep improving, but he's played great tennis the whole of last year, made a big improvement and I think now I have started to improve.

"I think it's because of those guys that I am playing as well as I am and I want to get to No 1. That's one of my goals for this year and I will try my best to do it."

Rafael Nadal, who meets Djokovic in the final today, can also see Murray becoming No 1 but believes the Scot lost the semi-final because he failed to play well in the fourth set, which he lost easily.

Nadal said: "Andy was unlucky and deserves to win a Grand Slam and the only negative was the beginning of the fourth. You cannot start the set like that against a player like Djokovic. He lost another very good opportunity."

Murray, the world No 4, is planning a training camp with Lendl in Florida – probably before the Indian Wells and Miami tournaments in March – and one key area for the eight-times Slam champion to improve will be the Scot's second serve. It needs to become a weapon rather than easy meat for opponents to feast on at key moments.

Murray added: "I need to practise in the warm weather and so as soon as I can I will go over to Miami and start working with Ivan.

"In four or five days' time when I talk to the guys in my team about the match and the last few weeks [he won the Brisbane title] I am sure I won't be as disappointed as I am just now, so I've got to try as best as possible to take all the positives from it."

Djokovic has already seen an improvement in his long-time friend's game after a short period with Lendl as coach. He said:"Andy was more confident on the court, taking chances and being more aggressive. I think he was playing better."