Chris Schofield and Gary Yates spun the Red Rose county to a superb innings and 35-run victory over rivals Gloucestershire at Old Trafford.
The pair shared another eight wickets on a turning pitch to lift Lancashire into third place, just two points behind Leicestershire and 20 adrift of leaders Surrey.
But Whatmore said: ``We know we're in a good position, but it won't affect how we play the rest of the season. The pressure won't get to us because, to be honest, I don't think we'll come under too much of it.
``The championship could go down to the last game because it is so close - and hopefully we'll be involved - but people don't expect us to win it. ``Lancashire haven't won this competition for many years now so people will probably not expect us to change that right now. Let's hope we can surprise them.''
Leg spinner Schofield took 4-60 to complete match figures of 8-116 and Yates contributed another four victims as Gloucestershire were skittled for 193 in the second innings. Schofield is still only 20 and that was his second appearance at first class level and Whatmore said: ``There was a huge responsibility on Chris because he was entrusted with bowling Gloucester out twice.
``That's a big challenge for an inexperienced player but he rose to the occasion and as long as he keeps his feet on the ground, he will have a big future.''
With Wasim Akram and 12th man Ian Austin off the field, Whatmore was called upon to do some emergency fielding as Lancashire tried to wrap up the game and he said: ``It was the first time I'd been out on the field in an English first class game and it brought back many memories.''