Mike Williamson and Scott Severin scored in extra time to see off a brave Barnet fightback and spare the Championship side's blushes.
But Mackay believes his players did well to cope with a Barnet side that refused to lie down against their more illustrious opponents.
He said: "If you come to Barnet and don't expect a tough game then it can come back and bite you and our players knew it was going to be a lively atmosphere so we made sure we countered that and that's why we came out on top.
"I think we can play better than that but I think Barnet had a real go and you've got to match their effort so that eventually the quality of the players shines through.
"We ended up with two goals and a clean sheet but you have to respect the opposition and how they play."
Barnet shaded the first half and almost took the lead when Albert Adomah fired just over after latching on to Albert Jarrett's first-half corner.
Watford had chances of their own and had the ball in the net with 20 minutes to go only for Tommy Smith's effort to be ruled out for offside.
But they had keeper Richard Lee to thank for a stunning save from Adomah's powerful drive which forced extra time.
The Hornets struck at the end of the first period when Williamson rose to nod in Jobi McAnuff's cross, and they sealed the win thanks to Barnet keeper Jake Cole allowing Severin's shot to slither through his legs.
But Barnet manager Ian Hendon refused to be downbeat and predicts better results to follow for his team, who have now lost both their opening games this season.
He said: "It was a good performance against a decent side and we can hold our heads high. If we keep performing like that someone is going to get a good hiding. It's a matter of time before we get on the end of one of these chances to get us on our way.
"It's a new start for everybody. We've got lot s of new players but it's my team out there and they are performing well, but the results aren't good.
"I can't fault any of the players tonight even though we had one or two out of position.
"The team performances have been good and everyone has settled. We look to our second league game on Saturday at home and we need to put on the same sort of show at again."