Johanna Konta did not lack for goodwill and support, even from her conqueror Angelique Kerber after losing her first – but possibly not last - grand slam semi-final in two sets here on Thursday – and should leave Melbourne filled with hope rather than despondency.

Making her main draw debut after previously failing to get out of the qualifiers, she was the talk of the tournament. She had played better than this in the fortnight but there was no denying Kerber deserved her victory.

The German left-hander pulled away from her in the second set to win 7-5, 6-2 in an hour and 22 minutes on Rod Laver Arena, and now faces the biggest challenge in the women's game: a final against Serena Williams.

Earlier, Williams threatened to embarrass Agnieszka Radwanska with a double bagel until the Pole gathered her composure in the second set. The American resisted the brief fightback to win 6-0, 6-4. As Radwanska said later, “I didn’t think that I was playing that bad. She just started unbelievable, with such a power and speed. I was just standing there kind of watching her playing.

“Everything was just too good, from her serve to her return. When I was serving, everything is just coming back to your side with that power, so deep that you cannot do anything.”

Kerber said courtside after the second semi-final: “This is a really special moment. I was trying to give everything today. Johanna had a great two weeks. She is a great player and has a great future. She will win many, many tournaments in the future. Thank you guys. I hope you will support me in the final.”

She might get it – and she will need it.

With the roof drawn back, it was plain the crowd were with Sydney-born Konta. They applauded her winners warmly there were collective groans when early jitters induced nine unforced errors inside the first quarter of an hour, Kerber breaking twice to lead 3-0.

Konta broke back to get on the board and the match at last took on the feel of a genuine contest. The ground strokes began to find their target. She hit her first ace after 20 minutes – to go with 21 for the tournament – and, with her best weapon clicking, she finally began to put pressure on the world No6.

Now Kerber struggled, and she was visibly annoyed when a backhand billowed the net on break point on her serve for 3-all after 25 minutes of absorbing, if error-riddled tennis.

While some members of the crowd lampooned Konta’s supposedly posh accent with shouts of “Jolly good show!”, she stuck doggedly to her task. This was her famous “process” kicking in as she stayed in “the moment”. All that had gone before was irrelevant. What was to come she would only know when she got there.

There was little between them after half an hour, although Konta’s serve was starting to click and the German did not seem so certain in the shot.

However, a double fault and a couple of loose forehands cost Konta her serve in the 11th game and Kerber served for the set – five minutes after an interlude to wipe a few drops of rain from the lines, in bright sunshine.

She held to love, securing the set with a neat chip down the line to end a quality rally.

When she broke again at the start of the second set, Konta for the first time expressed her frustration, banging a ball into the ground between serves. She desperately needed to inject some composure into her tennis because the errors were starting to flow with worrying regularity – 20 in the first set, to just six by her opponent at that point.

A break point in the second game gave her heart, but Kerber saved with an ace. The moment passed and the assignment grew harder.

Konta produced flashes of form but she struggled for consistency, off the ground and with her serve. She held for 1-2 just past the hour but, striving for depth and width, she gambled too often with the paint.

Konta threatened to get back in the contest in the fifth game but again her racquet let her down from the baseline, a netted backhand gifting Kerber a 4-1 lead. She held to 15 and Konta served to stay in the tournament.

To come back from this point would be some statement from the British No1, and she hung on to the slim hope, holding to 15. Could she break the solid German left-hander to extend her run, though?

Sadly for Sydney, London and possibly Budapest, the triple passport-holder with the winning smile, the tri-citizen and Jason Bourne of tennis, there would be no escaping Kerber's sound finish. A final backhand drifted long, her 36th unforced error, and it was done.

But what a debut Konta has had, the first British woman to reach the semi-finals here since Jo Durie in 1984. The crowd stood to acclaim her. They weren't bothered where she was from, but probably will take much interest in where she is going.

She leaves Melbourne with a ranking good enough to be seeded at the next slam, at Roland Garros.

(Guardian service)