The 29-year-old left-back was brought in from Fulham on Tuesday but has had little time to get to know his new team-mates as most have been away on international duty.
Konchesky played the second half of Jamie Carragher's testimonial yesterday, in which Liverpool comfortably beat an Everton XI 4-1.
But he accepts things will be a lot tougher when he makes his full debut for real, possibly next weekend at Birmingham.
"I'm 29 and this is my last chance to play at the highest level. That is what Liverpool are and I am really looking forward to it," said Konchesky, who has been reunited with former Fulham boss Roy Hodgson.
"It was a big factor (Hodgson) but Liverpool being a big club was a massive factor.
"I'm looking forward to getting a new lease of life and playing at a very high standard.
"I can't wait to pull on a Liverpool shirt in the Premier League, it is a massive club and it is a big step for me.
"I just want to give it my all and go from there.
"I've had three or four days' training and although there have not been a lot of players there it has been a good week and I am hopefully going to enjoy it soon.
"It was good to be involved in Jamie's testimonial and put a Liverpool shirt on."
Konchesky enjoyed his run-out in the relaxed atmosphere of a friendly but is looking forward to being able to bring success back to Anfield.
"You look at the history they have got behind them it is unbelievable and there are some great players here," he added.
"If we can bring that back to the side this year in something like the Europa League then this team can go a long way.
"The testimonial was a bit slower than the Premier League but it was good for Jamie.
"I'm glad all the players came back for him; they obviously respect him a lot and he is well respected within the team.
"He looks fit and I think he has a few more years left in him - and hopefully it will be at Liverpool."
Carragher, who hopes to raise £1million from the game and a gala dinner last night for his 23 Foundation, which benefits local groups and charities, is confident he will sign a new contract in the coming weeks.
"I don't think it has ever been in doubt," said the 32-year-old defender.
"The club has always been the most important thing and they will decide if they think I am good enough or not.
"I'm sure with the transfer window now closed maybe there is something we can sort out - I think it will take two minutes.
"I've always wanted to play for Liverpool for my whole career and I'm sure that will be the case."