The Uruguay international was named the Reds' player of the month - the third time in only six occasions he has been available for it - after scoring three goals but contributing much more.
However, the 24-year-old was keen to stress Liverpool's two wins and a draw are down not just to him but the players around him.
"I am very happy because I think the team has started really well and that is what we all wanted," said the Copa America winner.
"We are only three games in but we will be trying to continue in the same vein.
"The important thing for me is that the whole team is happy. It's just not about one player doing it on his own.
"I am happy when the team is winning and playing well.
"I think team spirit is very important. If we don't all get on with each other off the field then it becomes very difficult to achieve your targets on it.
"All of the new lads that have come in are helping us greatly, while at the same time getting on well with the rest of the squad.
"That's important, not only for the whole team but for the fans as well."
Suarez has had very little rest over the summer because of Uruguay's victory in their continental championship and manager Kenny Dalglish is keen to ensure his prized asset does not suffer accordingly.
The Scot rested the Uruguayan for the second match of the season at Arsenal only for him to come off the bench to score one and create the other in a 2-0 win.
Dalglish has said previously Suarez is keen to play in every game but the player himself admits there may be times when he has to be given a break.
"Whether I'm playing or not is something for the manager to think about, but it's true he also has to know when to rotate the squad a little on occasions," he told liverpoolfc.tv.
"But I like the style of play and tactics we've adopted in recent games, so I'm very happy."
Suarez is certain to start to Stoke on Saturday and there is likely to be a first appearance of the season for defender Glen Johnson, who was injured in Liverpool's final warm-up friendly against Valencia last month.
Captain Steven Gerrard is also close to making a long-awaited return after being sidelined since March after a groin operation.