The Murrayfield side are seventh in the table and face a difficult run-in as they seek a top-four finish.
"We have five huge games coming up and I think we need to win all of them if we want a shout of the play-offs or even the top six," said Dickinson, 32.
"It's really tight in the middle of the table."
Dickinson, with Willem Nel and Ross Ford part of an all-Edinburgh first-choice Scotland front row, has returned from international duty for the run-in.
The immediate target is a win in Wales on Sunday against Newport Gwent Dragons before a home match against second-bottom Zebre five days later.
Away games against Leinster and Munster follow before a Murrayfield date against Cardiff Blues.
"We have to think about winning every game, that's what we have to target, starting with Dragons away which is always a brutal encounter," continued the former Gloucester prop.
"It's a real tough run-in. We just have to take each game as it comes. We have a tough turnaround Sunday to Friday."
Asked to pinpoint what has led to Alan Solomons' men losing five of their last six matches in all competitions, he replied: "It's hard to know exactly what's gone wrong.
"We have let ourselves down with errors, a couple of soft tries at times, which have killed us.
"Sometimes these breaks between the Six Nations (games) don't help, you lose a bit of momentum, but this morning we had a good session so we are looking at things we need to improve on, just little things.
"The guys who haven't been away with the national squad are good enough to win these games.
"It's just touching up on our detail and being clinical and finishing the opportunities that we get and in the last few games we just haven't managed to do that."

Anne Marie Waters, a former Labour activist and founder of the Sharia Watch pressure group, has previously called Islam "evil".
Her leadership bid has split the party, with some MEPs threatening to quit if she was allowed into the race.
But the UKIP National Executive Committee, which vets all would-be candidates, has allowed her to stand.
The other candidates to replace Paul Nuttall - who stood down after UKIP's poor performance in June's general election - are:
Voting papers will be sent to party members over the next few weeks and the new leader will be announced at the party's annual conference in Torquay on the 29th and 30th of September.
Ms Waters's leadership bid was backed by former English Defence League leader Tommy Robinson and she has previously been blocked from standing as a UKIP election candidate.
James Carver, UKIP West Midlands MEP, said he "sincerely hoped" Ms Waters did not win - but added that she should be allowed to stand.
He said: "Her train of thought, I think is going about it the wrong way... there are many British Muslims in this country and that is a good thing."
The party's former leader, Paul Nuttall, has previously said her views made him "uncomfortable".
Ms Waters believes her anti-Islam message, including a proposed ban on the burka, the closure of all sharia councils and a temporary freeze on all immigration, will strike a chord with many voters.
She has argued that UKIP could regain support if it had the "guts" to be "honest about Islam" and challenge the view that it had "nothing to do" with jihadist violence.
Last month, former leader Nigel Farage told BBC's Sunday Politics that "if UKIP goes down the route of being a party that is anti the religion of Islam, then frankly it's finished".
Edinburgh will probably need to win all five of their remaining Pro12 matches to secure a play-off place, claims loosehead prop Alasdair Dickinson.
[NEXT_CONCEPT]
An anti-Islam candidate has been allowed to stand for the UKIP leadership.