McLeish was not exactly welcomed with open arms at Villa Park following his controversial summer defection from Birmingham and defeat in his first competitive match in charge would have provided ammunition to his critics.
And but for new signing Given, that could easily have been the outcome on Saturday, the Republic of Ireland star making several saves in what was otherwise a pretty dire goalless draw.
McLeish said: "The bottom line is, when there was all the furore, I always said it's about results.
"We started the league with a very good away point."
He added of Given, who Villa rescued from his Manchester City nightmare last month: "His experience tells him when to go into the right positions.
"You might have seen other goalies diving for one of the two that came point-blank at him, but that's the experience of a great goalkeeper."
McLeish denied Given was solely responsible for today's draw.
He said: "I don't think it's fair to say that. I would never say that.
"It's a team game and the team contributed to that point."
In fairness, Villa's defence also stood up pretty well to a side which was battle-hardened following their run to the Europa League play-off round.
"It was some great defending, people launching themselves to block balls on the edge of the box," McLeish said.
"That's terrific for the cause and the fans will love players who do that."
Any antagonism towards McLeish from the hordes of travelling Villa fans was drowned out by their new-season optimism as they gave team and manager a rousing reception as they entered the field.
"I was very, very pleased to walk across the turf and the Villa fans were very appreciative," McLeish said.
"I was delighted with it.
Supporters would have left ambivalent about what they saw, with Fulham goalkeeper Mark Schwarzer not having had a serious shot to save.
But McLeish insisted a draw was a good result.
"I don't consider it a bad one, that's for sure," he said.
"Anyone coming here, I think will find it hard.
"Fulham have taken some massive scalps at Craven Cottage over the years."
Indeed, despite the home side having had the better of the chances, it was actually McLeish's opposite number who was unhappy with the performance of his players.
Martin Jol gave the Cottagers a mark of only "six and a half" out of 10 for what was also his first Premier League game in charge.
He said: "We had three good chances but, for a home match, I would like to have more control, more initiative and we have to score at first.
"So, 0-0 at home, you can't say that is a very good result."
He added: "The first half, I thought they kept the ball better than we did and we looked nervous.
"We didn't keep the ball well enough for a home game.
"But the second half, especially the first 20 minutes, was good.
"If you're in their half, you have to keep the ball, and that is what I thought we did better in the second half."
Bobby Zamora and Andrew Johnson were both thwarted by Given after the break but it was a first-half miss from debutant John Arne Riise that was arguably most costly.
Jol defended the summer signing, saying: "If he had passed it into the net, it would've maybe been a save."
Fulham did manage to stop Darren Bent getting into the game at all, something that particularly pleased former Tottenham boss Jol.
"I probably know him better than most people because I had him at Spurs," he said.
"He's always dangerous for 90, 95 minutes."
Jol was also delighted to be back in the Premier League after almost four years away.
"It was a great feeling," he said.
"If you look at the figures, it's totally different from other countries, financially, player-wise."
And the Dutchman confirmed he would continue to use the limited finances at his disposal to recruit players before the transfer window closed.
He said: "Hopefully, we can do something in the next few weeks."
Source: Team Talk
Source: Team Talk