Kamara put Udinese ahead in the 29th minute before Douvikas levelled midway through the second half, with both sides missing further chances to win it, including a golden opportunity for the hosts in the 88th minute and a Ramon effort that struck the crossbar in stoppage time.
Fàbregas, whose side made their Serie A bow with three summer signings — Trevoh Chalobah, Yan Couto and Luis Milla — all thrown straight into the starting XI, praised a tighter, more open contest under this season's new refereeing guidelines.
"Yes, it was a good match, maybe a so-so one for the coaches, but I really enjoyed it as a game. The new rules raise the level of the match a lot. Someone might pull a muscle, someone might get hurt, and today that happened more to Udinese than to us.
"But that makes substitutions even more important. I understand that Jesus Rodríguez had to stay down for a minute after that knock, because it was clear the lad was hurt.
"Certainly these are rules that bring something good."
Asked about Nico Paz and Nicolás Baturina frequently occupying tight central positions together, Fàbregas explained it reflected an evolving tactical picture rather than a fixed system.
"We've already played with Baturina and Nico Paz close together at times. Every match we change something small, but this year we need to get used to having a very strong identity aside from the tactics. We're coming off seasons with full weeks to prepare, but this year there will be times when we won't be able to train as much."
The Como boss singled out Chalobah's performance for particular praise, alongside a rapid impact from substitute Mattia Liberali.
"I think Chalobah had an incredible match. Liberali also came on very well, he has something special, I like him, he has personality. We were smart to pick up an Italian diamond — let's not forget he's only 19. I understand very quickly when someone is a bit behind, he's the type who says 'give me everything and I'll respond.' We picked up a point on a very difficult ground, a word I don't usually like to use.
"You'll see that few teams will win here this year, they're a very good side, they have identity, they're physical, the way they press and move quickly is Premier League standard."
Chalobah, speaking separately after his full Serie A debut, said the step up in intensity had matched his expectations.
"It was a difficult game today, against a strong team, a bit in the Premier League style. We played better in the second half, building more, the impact was good, I can't wait to play this season in Italy."
The centre-back also pointed to Como's threat from set-pieces, with Milla's delivery a source of promise, "I think it'll be one of the strengths of our game, we won a lot of corners today, Milla with his quality will definitely help us."
Asked whether the point represented satisfaction or frustration given how close Como had come to victory, Chalobah was pragmatic.
"We're certainly not happy we didn't win, but it's difficult to come here and get a result. Either way we picked up a good point, and we look ahead — we're working for the game against Napoli."
Fàbregas also fielded a question on the club's late transfer business, including reported interest in Fiorentina's Moise Kean, without confirming any specific move, "I don't think much about the market, matchday is my joy. I'd prefer the market to close a couple of days before the Serie A opener."