Lambert completed a £3million move to Albion on Friday and scored twice in a friendly win over Bristol Rovers just hours later.
The 33-year-old started just seven Premier League games after joining from Southampton last summer – and has hinted he was not happy with his lack of chances.
He told The Sun: “I’ve got a lot of feelings, to be honest.
“But I’m not going to get into it right now. I don’t think it’s the right time.
“There is plenty of time to say exactly how I feel but at the minute, I’m just enjoying the fact I’m a West Brom player.”
Lambert’s lack of playing time for the Reds saw him lose his place in the England squad, but he has set his sights on winning a recall ahead of the Euro 2016 finals next summer.
“I will never give up,” Lambert added. “My character and personality won’t allow it. No one expects me to achieve that but you have to believe in yourself.
“If I have a season like I did at Southampton, there’s no reason why I can’t get back in.
“You’ve got to remember, it’s only two years since I scored 15 league goals and then 13 goals in a season.
“I’ve just got to make sure I get back to that.
“I feel like I’m going to play here. If I do, I’ll get chances. And if I get the chances, I think I will score goals.”