Suarez scored Barcelona's opening goal in a 3-0 win at Camp Nou last week, with Lionel Messi adding a brace to put the LaLiga side in complete control.
Some Liverpool supporters were upset with the way Suarez, who spent three and a half years at the club, celebrated his goal gleefully by sliding towards the corner flag on his knees.
Suarez gestured an apology towards the Liverpool fans before the restart and he confirmed he will show restraint if he is on target again in Tuesday's return fixture at Anfield.
"People who love this sport know the importance of a goal in the Champions League semi-finals," Suarez told a news conference.
"I have all the respect in the world for the Liverpool fans. I am very thankful to them. If I score a goal against Liverpool here I won't celebrate in the same way.
"Being at Liverpool helped me in so many ways, it made me more professional, it helped me mature. Having players here with great experience allowed me to be better even more. Being captain of Liverpool was one of the proudest moments of my career. I won't forget it.
"The reason I am playing at Barcelona, at the elite level, is because of Liverpool. If I score tomorrow it will mean I can feel relaxed and Liverpool have to score more to qualify. But it won't relax me on a personal level. It's not about me getting more goals on my account.
"I was never not up for games at Anfield. You'd play a game against a lower league team in the cup and the stadium would be full and it motivated you. If there was nothing on the game, it would still be full. The motivation is different now as I'm in a different shirt.
"All the work I did here and the way I'm thankful for Liverpool... the team had four or five years without being in the Champions League, the people here know the work I did here. I think there will be more applause than whistles for me.
"I think there will be some people unhappy but there are people in the kitchen [at training centre Melwood] waiting to give me presents for my children. It was the first stadium for one of them."
Suárez: "Anfield is always special. It's very nice for me to come back here, because thanks to Liverpool I've experienced some wonderful moments" pic.twitter.com/Ssq0fYh1OC— FC Barcelona (@FCBarcelona) May 6, 2019
While Barca's commanding lead puts them in pole position to reach the final, their stunning exit against Roma at the quarter-final stage last year – when they surrendered a three-goal advantage on Italian soil – remains fresh in their minds.
"You learn from your errors. We were too relaxed," Suarez said. "If you switch off for 30 seconds they can score and that warms up the fans. We need to be conscious of that to ensure it doesn't happen again.
"We don't have to be complacent entering into this tie. The result doesn't tell the whole story, they created a lot of chances. It could have been 4-1 or 3-1 at the end. You have to know what it's like playing against a team who got to the final last year."