Matteo Berrettini was proud of the bravery he displayed against Rafael Nadal in a US Open experience that has convinced him he "can be really dangerous".

World number 25 Berrettini's hopes of reaching a first grand slam final were dashed by a 7-6 (8-6), 6-4, 6-1 defeat to Nadal, who is one win away from his 19th major singles triumph – one fewer than Roger Federer's record.

The 23-year-old Italian, who has claimed two ATP Tour titles this year, was pleased with his run to the semi-finals at Flushing Meadows and the tennis he played, having struggled with an ankle injury since his fourth-round exit to Federer at Wimbledon.

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Asked what he would take away from his efforts in New York, Berrettini said: "A lot of things, I guess. First of all, I'm still learning the tennis. It's really weird. I was coming here with not a lot of confidence. I was injured. I didn't play a good match in Cincinnati [in a loss against Juan Ignacio Londero]. I didn't expect to do such a great tournament.

"I'm learning to be ready. Every match is important. Every point is important – this one for sure. Then all the matches, you have to be focused and ready to get the chances that you're making.

"I think when I have the right attitude on the court, I can play with any guys. If I'm focusing, if I'm playing my tennis, I can be really dangerous. That's really important to have this confidence."

The meeting with Nadal could have gone very differently had Berrettini been able to convert either of the two set points that came his way in the opening tie-break.

"Winning the first set would have meant I think a lot. Especially with him, it's tough to go a set down after an hour, more than an hour, with him," he said.

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"But I was feeling I was playing really good, even though he had a lot of chances on my serve. I think I played also good important points. I mean, I was brave, like I asked of myself.

"I couldn't say anything bad. I cannot complain about what I did. I was playing with Rafa, centre court, in the semis. I think it's okay."

Berrettini, who lost in straight sets and took just five games against Federer at Wimbledon, added: "The last time I played one of the big three [it] didn't go that well. The feelings I had on court for sure was an unbelievable experience. I didn't have so many chances. I think I learned a lot from the match in Wimbledon.

"I was more ready. I was feeling also that the next time I'm going to play Rafa, I'll be more ready because I didn't ever play him even in practice. I didn't know what to expect a lot.

"I think this match will help me a lot to improve my tennis, my everything, and for sure be ready for him the next time."