An 11-match unbeaten run towards the end of 2011 had left some claiming the current Spurs group were on a par with the 1961 double-winning squad.
Manager Harry Redknapp suggested a sustained tilt at their first title in 51 years was possible after the club went within touching distance of the summit in January, but Tottenham's season is on the verge of imploding in spectacular style.
The Londoners have won just one of their last eight Barclays Premier League games and were knocked out of the FA Cup in controversial style thanks to Chelsea's 5-1 victory at Wembley.
In a frank interview which followed the thrashing, Parker conceded that after starting the season so well, it would be a failure if Tottenham could not bring Champions League football to White Hart Lane next term.
"If we don't end up fourth we will have failed as a squad," he said.
"We've had a fantastic ride this year and we've dipped, that's obvious.
"Even our own manager is probably doubting us a little bit at the moment. Others (are), too, like our own fans."
Redknapp said last week that his team's form was "fantastic", claiming the club's poor results were due to a combination of bad luck and the fact that they had faced some of the league's toughest teams like Chelsea, Arsenal and Manchester United.
Yet poor displays in their draws against Sunderland and Stoke, and in last week's home defeat by Norwich, have left others claiming the speculation surrounding Redknapp's future and a potential switch to the national side is to blame.
Parker does not think that is the case but is still at a loss to explain how a team that played so well in the first half of the season has suddenly collapsed.
"Has the speculation about the manager affected us? I wouldn't like to think it had," he added.
"It's probably a combination of a few things: dip in form, a bit of tiredness, but we need to try to stay mentally strong and grind it out now."
Chelsea were helped along their way on Sunday by Martin Atkinson's decision to allow Juan Mata's strike to stand despite the fact that the ball did not cross the line.
Tottenham, who were left exposed at the back as they sought to close a two-goal gap, were incensed with the referee for allowing the Spaniard's effort to stand, but Parker now says the incident may help, rather than hinder the club in the long-run.
He said: "Something like yesterday's [Sunday's] result might just kick us on.
"We can try to get that siege mentality. We need to stand up and be counted and show the fans and show the manager that we're going to try to end up in fourth place.
"We've had a few hard-luck stories but we can't look back at those now.
"We have five games left and we need to win those.
"We haven't got 20 games left where we can sit down and analyse where we're going wrong. We need to try to stay positive and grind out the rest of the season and get fourth."
Redknapp revealed earlier this season that defender William Gallas, who has won two league titles with Arsenal, had given a pep-talk to the players, telling them they were capable of winning the division.
The Frenchman has now downgraded his expectations and admits Tottenham still have a lot to do to finish fourth ahead of Newcastle, with whom they are level on goal difference, and Chelsea, who trail by two points.
He said: "We have to improve a lot. Even if we have good players and a good squad, it showed for example today [Sunday] or earlier in the season that we are not ready yet. We have to work more and more.
"After this, Chelsea will be strong and they will finish the season very well, so we will have to finish it very well, too."