"I am aware that in recent matches that I played I've been calmer," he said on his return to Uruguay ahead of crucial World Cup qualifiers.
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Suárez with newborn son Benja on Saturday
"I am very self-critical and I realised that playing well, with more tranquility, is helping me a lot.
"I realise and I prefer to continue and not be the same as before."
Suárez surprised many by appearing on the field with his children, but it is something of a tradition among South Americans and, despite initial resistance from club officials, they gave way on the striker's insistence.
Luis Suárez Controversies
(01 of18)
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Suárez stops the ball with the hands during the extra-time of Uruguay's 2010 World Cup quarter-final match with Ghana... (credit:Getty Images)
(02 of18)
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He is shown a red card after his handball by referee Olegario Benquerenca, but Asamoah Gyan misses the spot-kick... (credit:PA)
(03 of18)
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And Uruguay go on to win on penalties as Suárez is demonised by the Ghanians (credit:Getty Images)
Dutch Eredivisie - Bite incident Luis Suarez(04 of18)
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Suárez was not sent off for biting PSV Eindhoven midfielder Otman Bakkal's shoulder while Ajax captain in November 2011... (credit:Getty Images)
(05 of18)
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But he did receive a seven-match ban (credit:Getty Images)
(06 of18)
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An early glimpse of Suárez's nature came in March 2011 when, after a Rafael da Silva tackle on Lucas Leiva, he slyly tugged the Brazilian's hair in a bid to wind him up (credit:Getty Images)
(07 of18)
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Suárez feigns agony as Jack Rodwell is erroneously sent off by Martin Atkinson in the October 2011 Merseyside derby. Liverpool win the game 2-0 and Suárez scores. (credit:PA)
(08 of18)
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Later in October, a foul by Suárez on Patrice Evra sparks off his most infamous misdemeanour... (credit:Getty Images)
(09 of18)
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When he racially abuses Evra, calling him a "negro" eight times... (credit:Getty Images)
(10 of18)
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Suárez is fined £40,000 and banned for eight matches (credit:Getty Images)
(11 of18)
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Suárez is suspended for one game for making an offensive gesture to Fulham fans in December 2011.
(12 of18)
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On his first start since his ban for racially abusing Evra, Suárez refuses to shake his hand in February 2012 (credit:PA)
(13 of18)
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Suárez executes a pathetic dive in a 0-0 draw against Stoke in October 2012. He later admits to cheating (credit:AP)
(14 of18)
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Bemusing irony as Suárez opts for a diving celebration in front of Everton manager David Moyes, who accused the Uruguayan of simulation after the Stoke tumble (credit:PA)
(15 of18)
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Suárez is fortunate not to be red-carded after he rakes his studs down Sylvain Distin's heel in the same game. Everton fans enjoy poetic justice when he scores a late header which is wrongly disallowed for offside (credit:PA)
(16 of18)
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Suárez controls the ball with his hand at Mansfield Town to score Liverpool's winner in the third-round of the FA Cup, January 2013 (credit:AP)
(17 of18)
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Chewy Suárez: A shocked Branislav Ivanović reels from being bitten by the controversial striker (credit:Getty Images)
(18 of18)
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Giorgio Chiellini shows off the bite mark from where Suárez bit him. (credit:Getty Images)
"In England it is not common and the first club people told me I was not going to go with them but I told them that my children were going to come with me, like it or not," he told reporters who greeted his arrival at Montevideo airport in comments reported in Uruguayan newspaper El País.
"They understood in the end and it was a nice moment, a unique moment for me.
"They (family) make me think hard and calm me. Nowadays I think a lot of them when I'm on the field.
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Suárez scored on his Anfield comeback against Crystal Palace
"I wanted my son to live as I do. I suffered a lot as a child and I do not want my children, or any other child, to experience the circumstances as I did.
"As a parent I try to give them all the love in the world and all the best."
Suárez dismissed some suggestions in the media that he had used his children to help win over fans on his first appearance at Anfield since the furore of his summer transfer saga when he accused the club of reneging in a deal allowing him to leave for a Champions League side.
"What the English papers say I do not care," added Suárez, who earlier in the summer had cited the British media as being one of the reasons he wanted to leave.
"The only thing I care about is playing football, and enjoying my family is what I love most."