The European Ryder Cup veteran, who became one of the most high-profile defectors to the controversial Saudi-backed circuit last month, also criticised the media for "stoking up" arguments between people on both sides of an increasingly bitter row.
That came after Phil Mickelson, another star LIV signing, showed his frustration with reporters after being asked about his own situation.
Woods said earlier this week that players had "turned their back on what allowed them to get to this position" by signing up to play in LIV's big-money events.
Asked about the 15-time major winner's comments, Westwood said: "He's got a vested interest hasn't he?
"The LIV players will talk the LIV tour up, the PGA players that aren't on the LIV tour will talk the PGA Tour up and put down the LIV tour.
"I don't pay too much attention to people's opinions. Tiger is entitled to his opinion."
The PGA Tour has suspended players who have joined LIV while the European-based DP World Tour has also imposed sanctions.
Amid the escalating dispute, another LIV player, Ian Poulter, was booed as he prepared for his first shot at the Open.
Westwood did not experience any hostility during his opening round of 68 and claimed it was wrong to suggest he would.
"I don't think it had the potential (for that)," he told reporters. "I think the media are stoking it up and doing as much as they can to aid that, but I think the general public just want to go out there and see good golf, no matter where it is being played or who is playing it."
When a journalist said the media was not doing that, Westwood responded: "We could stand here and argue all day but it is.
"I have spoken to a lot of people who were there last week and there is no animosity between players, but there are stories being written that there is.
"You are creating issues where there are none. If you want to do it that way, fine."
Mickelson earlier snapped after fielding a number of questions about his absence from this week's celebratory past champions events at the 150th Open.
Organisers the R&A hosted a dinner for previous winners and invited a number to participate in a four-hole exhibition competition.
The R&A made abundantly clear LIV figurehead Greg Norman, the Open champions in 1986 and 1993, had not been invited to prevent his presence becoming a distraction.
Mickelson insisted that had not been the case for him but he declined to attend out of respect.
The 52-year-old, who won at Muirfield in 2013, said: "The R&A contacted me a couple weeks before and said, 'Look, we don't think it's a great idea you go, but if you want to, you can'.
"I just didn't want to make a big deal about it, so I said, 'fine'. We both kind of agreed that it would be best if I didn't."
Asked if he was sad to be in such a position, the veteran American said: "No, no. Not at all. I think that I couldn't be more excited and ecstatic with where I'm at.
"I love the events. I get to have golf in my life and competitive golf in my life on a scale that is fun, exciting, different, and lets me play and compete but still do the things outside that I want to do."
Pushed further on missing the dinner, which was attended by the likes of Jack Nicklaus, Tom Watson, Sir Nick Faldo and Woods, Mickelson said: "Let it go, dude. Let it go. That's three times you've asked the same question.
"I don't know what to tell you. I couldn't be happier."
Mickelson, who opened with a level-par 72 at St Andrews, insisted he had no regrets about signing up for the big-money LIV circuit even though it has led to his exclusion from the PGA Tour.
He said: "I made the right decision for me and I'm excited about having the opportunity to play competitive golf and have it in my life in a more moderate scale to where I can do some things outside of that too. I freed up a lot of other time as well.
"I couldn't be happier. I think it's been really good. I can't wait to get to New Jersey and play another event there."