The 41-year-old trainer sent a message of support to the Frenchman and insisted he is not worried that Real Madrid may slip up in Wednesday's derby against Atletico
The French defender has been on the surgery table for over 10 hours, undergoing a liver transplant, with Barca's fans offering their support to the player with a standing ovation in the 22nd minute of the match.
"I would like to dedicate this victory to Abidal and his cousin, Gerard [who acted as a donor]," Guardiola told reporters after the match.
"This was a special day for us. We have to be prudent and wait for the next few days.
"We will see how he recovers next week. We are very thankful to the doctors and we have faith that he will keep going forward because he is a strong lad."
The victory provisionally puts the Blaugrana one point behind leaders Real Madrid ahead of Los Blancos' match against Atletico Madrid on Wednesday, but Guardiola is not thinking about a possible slip-up from the Spanish capital club.
"We did what we had to do, there is nothing we can do about the rest," Guardiola said.
"We had a good match and now we have to focus on the hard matches we have ahead, especially the ones away from home.
"The matches against Levante and Rayo Vallecano will tell us a lot about our future."
Guardiola then seemingly played down the comments from former Barca coach Carles Rexach, who said earlier on Tuesday that Madrid were crumbling under the pressure that comes from being leaders.
"Clubs at this level have the right pressure," the 41-year-old said. "I did not watch their match against Villarreal, but they could have won their games against Malaga and Valencia."
Lionel Messi scored on Tuesday his 59th official goal of the season, and Guardiola thinks that the Argentine can go even further.
"He is capable of reaching the 60-goal mark," the coach noted. "The most important thing is that he had another great match tonight.
"His goal helped us getting calm. It was not easy for his team-mates to find him on the field but they did it."