The 28-year-old seamer took 5 for 62 as Australia, set a colossal 538-run target, were bowled out for 164 on the fourth afternoon in their worst-ever defeat against Pakistan, losing by 373 runs at Sheikh Zayed Stadium.
Abbas finished with 10 for 95 for the match after taking 5 for 33 in the first innings, ending up as man-of-the-series with 17 wickets in two Tests.
Sarfraz claimed Australia weren't ready for Abbas, who was also named man-of-the-series on Pakistan's trip to England earlier this year.
"Looks like they hadn't prepared for Abbas, they took him a little easy," said Sarfraz.
Australia entered the two-Test series focused on the threat of leg-spinner Yasir Shah, although he managed just eight wickets.
"But credit goes to Abbas, because the pitch is not suitable for fast bowlers," said Sarfraz.
"The way he bowled, he was the best bowler on either side. The way he bowled throughout he was the main factor for us winning the series."
Abbas took seven wickets in the first Test which Australia drew after a determined fightback on the fifth day in Dubai.
Sarfraz said both teams were missing experienced players, with Pakistan's Test unit in a transition phase after last year's retirement of senior batsmen Younis Khan and Misbah-ul-Haq.
Australia were without key batsmen Steve Smith and David Warner -- both banned a year for their role in the ball-tampering scandal in South Africa in March.
"I am not so surprised at this win," said Sarfraz. "Both teams are missing senior players. The way my team played the first match, we almost won it but couldn’t. The way we recovered from 57-5 on day one was remarkable."
Paine agreed with Sarfraz's assessment of Abbas, the first Pakistani fast bowler to take a 10-wicket haul in a Test since Mohammad Asif against Sri Lanka at Kandy in 2006.
"Abbas is a world-class bowler," said Paine.
"He (Abbas) challenged our defence and was too good for us. Yasir didn’t get the wickets, but he bowled just as well. Over here, one of the things our bowlers talked about was building pressure from both ends. That is what Pakistan did really well together."
Paine, who took over the captaincy in the wake of Smith's suspension, said the defeat was "hard to swallow".
"It's bitterly disappointing, no doubt. We had some momentum from the first Test, started really well here but it went a bit pear-shaped to be honest all over the field," he said.
"It's hard to swallow. We came here to win this series and we did OK in the first Test and showed at least some fight and showed the style and brand of cricket we wanted to play."
Pakistan and Australia now head into a series of three Twenty20 internationals, with the first in Abu Dhabi on Wednesday.
First Published: October 20, 2018, 9:42 AM IST