The Uruguayan has enjoyed an excellent start to his Reds career after joining in January from Ajax but he is hopeful he will continue to improve and help his team move up the league table.
"I am very pleased because it is important for a player to have the supporters' recognition that they are doing a good job," Suarez told the club’s official website. "However, the main thing is that the team continues to pick up points.
"I think I can still keep improving and offer that little bit more. I am happy at how the team is playing as a whole, but from a personal point of view I'd love to be able to provide that bit extra for the team."
Suarez feels Liverpool had the best of the game as they drew 1-1 with Manchester United at Anfield last weekend and believes they should have won the match.
However the striker thinks the team can take confidence from how they played against the Champions into their coming Premier League fixtures.
"We could certainly have gone on to win the game," said Suarez. "We had more opportunities to score than they did. I think they had one or two, but we had four or five really good chances to win it.
"The main thing is the team played well and we are pleased with the performance - it shows promise for the rest of the Premier League campaign.
"We're certainly capable of beating anyone," he added. "The team is in good form and feeling very confident, and it's also good the manager can see we have the ambition to pick up trophies.
"But for now, we'll take each match as it comes and hope to pick up some victories in the next few games."
The Uruguayan thinks the Reds new signings have helped them improve this season and he feels they have gelled well as a team so far, and is hopeful he and his team-mates can get a result on Saturday against new-boys Norwich City to take them further up the table.
"I think the new arrivals have all been positive additions that have helped the team a lot," said Suarez. "Although they know they are key players, the main thing is all of the squad knows we are in it together. No one player is bigger than the rest - on the field we are all equal."
Suarez added: "I hope we can get back to winning ways against Norwich. It's an important match in front of our own fans, so let's hope we can grab all three points and put a smile on everyone's face."