A dozen or so Coventry supporters - frustrated by off-field events at the crisis club - went on to the Broadfield Stadium pitch and held up play for three minutes after seeing their side go 2-0 down midway through the first half.
City battled back from going behind to goals from Jamie Proctor and Joe Walsh, with Callum Wilson and Franck Moussa scoring, before midfielder Mike Jones gave Crawley a 3-2 victory six minutes from time.
Pressley admitted the Football League`s 10-point deduction on Friday had come as a "hammer blow" to the club but he was more determined than ever to see his job through.
Coventry, with CCFC Ltd facing liquidation, had the backing of over 1,000 travelling fans and Pressley said: "The vast majority behaved brilliantly. I hope there won't be any action taken because of the pitch invasion.
"If you become a football manager you have difficult cards. Coventry City is a great club and over the past four or five months a lot of politics has gone one, but I`m determined to lead us through this difficult period."
A long-running rent dispute between Coventry and the management company behind the Ricoh Arena will see the Sky Blues play their `home' games at Northampton's Sixfields Stadium this season while a new ground is being built.
Pressley says he has great sympathy with the supporters but insists his resolve is stronger than ever, adding: "Over the last 15 years we haven`t finished higher than eighth and we must improve.
"We are thin on the ground because of the transfer embargo and we could do with getting some players in. But it is going to be step by step for us.
"I`m exceptionally proud yet disappointed that we didn`t win at Crawley. We`ve had to endure a great deal in the past months and losing 10 points is a hammer blow, but we showed great character and at 2-2 we were capable of winning the game."
- Sports & Recreation
- Franck Moussa
- Callum Wilson
- Coventry City