The advice used to be 'ignore it and it will go away'.
This is no longer quite so certain - the Protection of Freedoms Act (2012) makes it much easier for these companies to take legal action against the registered keeper of the vehicle to enforce parking charges.
Some companies are energetically doing this and getting judgements in their favour (costing the driver/keeper much more than the original penalty charge).
The balance of probabilities is still in favour of 'ignore' - but you are taking more of a risk than in the past.
As a matter of interest - what exactly did the company say you did? If it was 'over time limit' then it's often possible to disprove this with other evidence. If it was 'parked in disabled space' or 'caused obstruction by parking not in a bay' then without a photo they have no case.