The Reds played out a tense goalless draw with reigning champions City at Anfield on Sunday, which left the two sides level with Chelsea on 20 points at the top of the table.
Arsenal and Tottenham Hotspur sit just two points behind the leading pack, too, and Robertson expects the race to involve several teams throughout the campaign.
He does believe Liverpool will be one of them, though.
“We feel we can compete with any team but people seem to be just dismissing other teams and making it a two-horse race, which is not the case,” the Scotland international told Sky Sports.
“We played Chelsea last week, who were excellent. They have been on a great run. You see teams like Arsenal, with a new manager, putting great results together.
“So there is a long way to go and there will be a lot of teams competing but we hope we are one of them.”
After four goal-filled meetings with City last season, the latest clash between Jürgen Klopp and Pep Guardiola’s men failed to spark in similar fashion.
But Liverpool, who were determined to bounce back from their 1-0 defeat against Napoli, received a let-off when Riyad Mahrez sent his 86th-minute penalty over the crossbar.
Reflecting on the stalemate, Robertson added: “We started well. We were all disappointed with Wednesday as a 90 minutes as a whole, so we wanted to get off to a fast start.
“They struggled to get a foothold in the first half. They probably controlled it a bit more in the second half and had a bit more composure when we were rushing it.
“There was nothing really in the game – it was two really good teams going at it. Unfortunately, the deadlock wasn’t broken.
“But for us it’s another important point, especially going into the international break with a long break until the next game.”
Watch: Extended highlights from Anfield
Klopp shuffled his defence for the visit of City, with Dejan Lovren brought into central defence and Joe Gomez moved from the middle to right-back.
The Reds extended a remarkable run of not conceding a Premier League goal at Anfield – which stretches back to February and now totals 841 minutes of football.
“As a back four, that’s what we go into every game going for. It was nice to keep hold of it,” said Gomez of the clean sheet.
“We had our chances as well; it’s not as if it was their game for the taking. It was with the penalty but we had good chances as well.
“As a unit, it’s all of us. We defend so well as a team; it starts from the front with the work-rate they put in. We want to do it collectively.”