McCall's men started strongly at the Stadio XXV Aprile and the former Heineken Cup winning centre with Ulster says that had a lot to do with the fact that last season's semi-finalists refused to underestimate their underdog opponents.
"What pleased me most this week was how good our preparation and mentality was," said McCall, after Saracens bounced back from a narrow defeat to Toulouse at Wembley last time out.
"We actually gave them a lot of respect in the build up to today's game, and we knew how difficult today could have been.
"Monday, Tuesday and Thursday training was at a very high level and I suppose we have to do the same this week and make sure we have the correct attitude, which I'm sure this group will."
Sarries led 25-0 after just over half an hour in Italy as George Kruis, Ernst Joubert and Chris Wyles all crossed early on and McCall was particularly impressed with the clinical nature of the opening period.
It took Saracens 61 minutes to secure the bonus point through the first score of Chris Ashton's quick-fire brace but McCall headed for home an understandably happy man.
"It was a really good performance because we did a very clinical job on Zebre, especially in the first half," added McCall.
"The energy of the group in the opening 35 minutes was outstanding, we took our chances when they were there.
"We made heavy weather getting the bonus point but you have to give credit to Zebre because they came out in the second half and fought really hard. So I'm delighted to have come away with the bonus-point win."