Fresh from winning the Copa America and being crowned the Player of the Tournament, Suarez returned to Melwood in fine form.
An opening-day goal against Sunderland was followed up by strikes against Arsenal and Exeter City.
It's the third time Suarez has claimed the Standard Chartered Player of the Month accolade - an outstanding achievement considering he only arrived at Liverpool in January.
However, upon being presented with the award at Melwood, the No.7 was eager to highlight the contribution of his teammates.
He told Liverpoolfc.tv:"I am very happy because I think the team has started really well, and that is what we all wanted. 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. 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.
"But I like the style of play and tactics we've adopted in recent games, so I'm very happy."
He added: "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."