Jurgen Klopp's side beat Tottenham to lift the European Cup back in June, after a thrilling journey through the knockout rounds.
A 2-0 victory ensured that Liverpool won the famous trophy for a sixth time, capping a superb season of progress which also included a second-place Premier League finish.
Klopp's men have picked up from where they left off this term, securing four league wins and another piece of silverware in the form of the UEFA Super Cup.
Wijnaldum feels that winning the Champions League has eased the pressure of expectation at Anfield, as he told Liverpool's official website: "Winning the Champions League has given us all peace of mind.
“Now we know what it’s like to win the biggest trophy of them all – and we just want to keep going from here and add even more titles.
“But Jurgen Klopp is not putting extreme pressure on us to win the Premier League. He does not tell us, ‘Now you must win this or that trophy’. He is very relaxed.
“He did not do that during the past season, either. His idea is that we get the maximum out of every individual every single day that we are together. And then we will see where that brings us at the end of the season.
“Just look at the list of world-class players who have not won the Champions League during their careers. It contains more famous names than you would think – and it tells you that it is really special we have won it with Liverpool.”
Virgil van Dijk was recognised by UEFA as the men's player of the year for 2018-19 during the draw show, ahead of Barcelona talisman Lionel Messi and Juventus superstar Cristiano Ronaldo.
The Netherlands international has also been tipped to win the Ballon d'Or later this year and Wijnaldum is "not surprised" that his fellow countryman is being singled out for individual awards.
“I was not surprised when Virgil won the UEFA best player award ahead of Lionel Messi and Cristiano Ronaldo. I actually expected him to win it,” the 28-year-old added.
“Virgil has had a blinder of a season and has been so successful. Nothing about him surprises me anymore.”