O'Leary was pleased with Villa's first win in six matches as they maintained their unbeaten home record to lift them back into the top ten.
"It was not a quality game but we managed to score twice to give us victory," he was honest enough to admit after the game.
The former Leeds United manager is still deeply concerned by the lack of depth in his squad and feels the Midlands club could become increasingly exposed in the winter period.
The loss of Darius Vassell in the second half was a big blow but the enigmatic striker continued to frustrate the Villa fans with his failure to get on the scoresheet despite his three goals in the previous two league games against Fulham.
O'Leary has stressed to Vassell that he needs to produce a better goals return but the England striker still struggled in front of goal and capped a miserable match by being stretchered off in the second half with an ankle injury.
Vassell certainly had an early opportunity to shine but his weak effort was easily dealt with by Edwin Van der Sar.
No-one can accuse Vassell of not trying and there is little doubt that he kept up some relentless pressure on the Fulham defence.
Fulham themselves suffered an early setback when they lost Ian Pearce, who over-stretched himself attempting to tackle Vassell and had to be replaced by Zesh Rehman.
In heavy rain, ball control was always difficult but Fulham were definitely off-key as they posed very few problems and the only real surprise was that it took Villa until the 26th minute to take the lead.
Lee Hendrie broke down the middle and was unceremoniously upended by Papa Bouba Diop. Fulham built a seemingly strong wall but Solano produced a perfect 25-yard free-kick that flew in to the top corner of the net just inches away from the desperate fingers of Van der Sar.
Vassell still battled without success to put his name on the scoresheet and, typical of his form, he latched on to a flick-on from Juan Pablo Angel just before the break, only to squander yet another good opportunity.
The big disappointment was the lack of attacking penetration from Fulham. In the first period they could only produce an off-target effort from Steed Malbranque.
Fulham might have earned themselves a second-half penalty when Claus Jensen's free-kick was deflected for a corner by the hand of Hendrie in a spell when Villa were at panic stations keeping out Fulham's best attacks of the match.
But the alarming factor so far as Villa were concerned was their inability to take complete control of a struggling Fulham side that rarely got into gear.
Following his four-match suspension, Andy Cole made an inauspicious return to the Fulham attack, receiving little change from the Villa defence in which Olof Mellberg was in commanding form.
Surprisingly Villa began to struggle in the second half when Vassell fumbled another golden opportunity and Fulham gained in confidence to take the game to the opposition.
Vassell then clashed with Bouba Diop and had to be stretched off and replaced by Carlton Cole.
Cole, told to keep on the straight and narrow by manager O'Leary only the previous day if he wants to become an international star, certainly made an immediate impact as he set up Villa's second goal.
The on-loan striker put a pass into the path of Hendrie who fired a long-range 75th minute shot past Van der Sar to seal the valuable three points for Villa.
It was the only real highlight of the second half when Villa lost their way until Hendrie's superb strike which sealed a well-deserved win over the struggling visitors.
MAN OF THE MATCH: Mark Delaney (Aston Villa) - The Welsh international produced a model performance. He linked up well with Olof Mellberg to effectively shut out the stuttering Fulham attack in which Andy Cole had an off-day.