Craig Brown's side are looking to bounce back from their 3-0 defeat at Inverness, which saw them slip six points off Caley Thistle and Motherwell in the race for second place in the Scottish Premier League.
Aberdeen also face Hibs at Easter Road in the last 16 of the Scottish Cup the following weekend as they look to end their 13-year wait for a major final appearance.
With an SPL trip to Perth to face St Johnstone in between, Robertson knows they need to get off to a good start when Hibs visit Pittodrie.
The left-back said: "This is a massive week for us, three games in seven days that could shape our season potentially.
"Hopefully we start the week off with a good result on Sunday.
"We need to get back to defending better and taking our chances up field, and we'll definitely win games with the players we have got.
"If we were to win the next two league games and the Scottish Cup tie we would go on a fantastic run and there is no reason why we can't finish high up the league.
"Sunday is crucial to give us confidence going into the other two games, against St Johnstone in the league and Hibs in the Scottish Cup.
"There is no reason why we can't. Everyone is capable of beating everyone in this league and we definitely have a strong enough team to do it."
Robertson has secured a regular starting spot in recent weeks after returning from the knee injury that ended last season prematurely.
The 19-year-old said: "I have started the last seven or eight games so it is good to get a run in the team and get some consistency going.
"I am starting to feel now that I am beginning to get back to my best form but there is still a lot more to come from me this season and I hope the fans will see that.
"I think the manager and Archie (Knox) know what I can do. They know themselves there is a lot more to come and so do I.
"But it has been hard being out for four months. I am getting back to full fitness and enjoying it so hopefully I will get a run in the team."
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