Saturday's 2-2 draw with Rob Roy left the Southside giants in eighth place with a third of their fixtures played, and Rich insists they face a monumental struggle to close the gap on the leading clubs.
He admitted: "Being defeatist is not in my blood, however I have to say that, barring a quite astonishing sequence of results, Pollok will not be crowned champions.
"As a team, we are most definitely getting better, as we showed in holding our own against a very good Rob Roy side last Saturday and, with everyone playing at their best, we are capable of taking points from any of the other teams.
"But we are a long way short of having the depth of squad to be considered a title challenger and, if I was a betting man, my money would be on the Rabs, Auchinleck Talbot, Petershill and, probably, Irvine Meadow, fighting it out for the top prize.
"Medda are the only one of the big four still to play us this season, and they are a little bit off the pace as things currently stand, but the very fact Chris Strain and his players have been over the course before could count in their favour.
"It's hard to see past Auchinleck given they remain unbeaten and have built up quite a lead at the top the table, however things can change so quickly in this game and we'll see how they react when the pressure begins to mount."
It merely underlines Lok's paucity of playing riches that Richardson admits to a string of injury concerns which leave his playing squad down to the bare bones for this weekend's crunch clash away to Beith.
He added: "I've had to pull us out of a friendly against Drumchapel Amateurs tonight because of the risk of picking up any more injuries. Steff Reilly aggravated a hamstring injury against Rob Roy and is facing at least a month on the sidelines, while Ross Hepburn picked up an ankle knock and Stuart Mills a calf strain.
"Darren Brady is awaiting surgery to cure a knee ligament problem and we are also slowly coming to terms with the latest bodyblow that our club captain Paul Lovering is facing a lengthy period out of action.
"He has been laid up with a viral infection which affected a knee, causing it to swell to twice its size and necessitated him being admitted to the Southern General Hospital last midweek where he went through an operation.
"As things currently stand, we don't know when he will be out of hospital, let alone ready to get back playing again."
Another setback is thought to be in the offing for Richardson after No.2 Stevie Docherty was ordered to stand on the terracings behind his dugout by referee Nick Walsh during the home game against Rob Roy.
At time up, Docco walked across the pitch in conversation with Richardson and was then summoned to Mr Walsh's room where he was given the equivalent of another red card for apparently re-entering the field of play.
Now the worry is that Docco – recently fined £100 for being sent off against Arthurlie – could be facing a lengthy dugout ban.