Redknapp had been the overwhelming favourite to replace Fabio Capello prior to this summer's European Championships.
However, it is Hodgson who will have talks with the Football Association on Monday after West Brom granted permission.
"No problem," Redknapp told BBC Sport. "I wish him [Hodgson] all the best. He's a great guy. I've got a great job here (at Spurs). I don't hold grudges.
"I've woken up in a great mood on the back of a great win yesterday (Sunday). I will be concentrating on Tottenham as I have done all along."
As news of the approach for Hodgson was confirmed on Sunday evening, Redknapp conceded his chance of coaching England had now gone.
"I can't see it (the England job) coming up for me now," Redknapp told The Times.
"Everyone else was saying I might get it but I never spoke to Daniel Levy (the Spurs chairman) about England."
Redknapp's plight has been compared to Brian Clough by some observers. Clough did not get the England job either when he was overlooked in favour of Ron Greenwood, which in retrospect looks like a huge mistake.
However, England fans' spokesman Mark Perryman does not believe the comparison is valid.
"It is a ridiculous comparison," said Perryman.
"Harry Redknapp has been a manager for 30 years and won one FA Cup.
"Brian Clough won two European Cups and lots of other trophies besides.
"To link the two doesn't stand up at all. Clough was the greatest manager never to manage England. Harry is the populist choice, but so was Kevin Keegan and what an unmitigated disaster that turned out to be.
"Roy Hodgson will be a steady hand on the tiller. He took Fulham to the Europa League final, which was a magnificent achievement and on the basis that the best three managers around just now, Marcelo Bielsa, Pep Guardiola and Jose Mourinho, wouldn't want the job, Hodgson is a good choice."
Hodgson is scheduled to meet the four-man Club England board - FA chairman David Bernstein, chief executive Alex Horne, director of football development Sir Trevor Brooking and Club England managing director Adrian Bevington - on Monday.
Providing there are no unforeseen problems, Hodgson should be confirmed as Capello's successor within the next 48 hours, although it is anticipated he would complete the Premier League season with West Brom before taking up his duties ahead of two Euro 2012 warm-up matches against Norway on May 26 and Belgium on June 2.
Hodgson certainly has plenty in his favour, including an impressive CV that boasts international experience with Switzerland, Finland and UAE.
As his West Brom contract is due to expire in the summer anyway, he would not cost any compensation either.
The fact he doesn't operate with a long-standing backroom team, unlike Redknapp, and is likely to spend plenty of time at the FA's impressive new coaching hub at St George's Park, also counted for Hodgson.