England midfielder Jordan Henderson and defenders Martin Skrtel and Dejan Lovren, of Slovakia and Croatia respectively, all said they had completed an excellent pre-season preparation with Sunday's 4-0 victory over Borussia Dortmund.
Each told Liverpool's website (www.liverpoolfc.com) of their happiness ahead of Sunday's Premier League meeting with Southampton at Anfield - and without a mention of last season's controversial top-scoring striker, who joined Barcelona in July for a reported 81 million euros ($108.40 million).
Suarez scored 31 goals for Liverpool to help them finish as runners-up in the Premier League, but was sold after being banned for four months for biting Italian defender Giorgio Chiellini while playing for Uruguay at the World Cup finals.
"It was a good way to end pre-season and get ready for next week," Henderson said on Monday. "Everybody is happy and hopefully we can continue that going into the game against Southampton.
"Most of our games in pre-season have been against top opposition, Champions League teams. Now we're ready for the real test next week. We're improving all the time. We continue to work hard and work on different things.
"We've got a young team that is developing very well and we've got a lot of experience despite being so young. Hopefully that will stand us in good stead for the season."
Ironically, three of manager Brendan Rodgers' new recruits will be in line to make their Liverpool debuts against their former club, Lovren having joined England striker Rickie Lambert and England midfielder Adam Lallana at Anfield.
"Lovren had a great season with Southampton and I am really happy that he is with us," said defender Skrtel. "We all need competition because that is what keeps you motivated.
"He will make us stronger, so I really welcome his arrival - and it will only make me work harder. Liverpool is not only about 11 players. We will have many games this season, so every player will be important."
Lovren, who scored with a typically powerful header and commanded the Liverpool defence with authority on Sunday, said his maiden outing for his new club had been 'amazing'.
"We're talking about Dortmund, who are in the Champions League every year and first or second in the German league," he said. "They are a quality team. We showed a quality style of football, with four goals and a clean sheet.
"It was amazing for us. We played very well and it was a good start for me also because I haven't had a long time with the team but I feel like I've been here for a month already."
Lovren added that he felt he had settled in quickly thanks to the similarity in style between Southampton and Liverpool.
"The coach (Rodgers) has a similar style to what I had before at Southampton, so it was much easier for me to adapt here," he said. "I'm really glad about that.
"I have another week before the Southampton game so (the whole squad and I) will have time to meet each other. But I've already settled down here."