The survey also revealed that just like youngsters, parents also do not have the time to follow their own interests and hobbies or even relax for a few moments.
Conducted to mark the launch of Disney's new parenting site UKfamily.co.uk, the survey showed that 84 per cent of mothers were 'physically worn out', 71 per cent were 'mentally worn out', and 68 per cent 'emotionally drained'.
Almost seven out of 10 mothers surveyed (68 per cent) said that they regularly "feel exhausted".
Having to meet the demands of both a work life and a home life, eight out of 10 stressed out mothers get less than an hour a day to themselves (77%), and 46 per cent of them get less than 45 minutes a day to themselves.
Those surveyed even said that their own mothers enjoyed far more free time when their children were young.
Only 38 per cent of grandmas had less than an hour a day to themselves, and 58 per cent enjoyed between an hour and five hours each day to themselves.
Forty-four per cent said that they enjoyed at least two hours or more a day to pursue their own interests when their children were young.
Grandads also fared much better than modern dads when it came to free time, with today's dads almost strapped for time as modern mums with six out of 10 (58%) having less than an hour a day to themselves.
Around 80 per cent of the fathers surveyed said that their own father enjoyed between two and six hours a day to pursue their own interests.
Although 90 per cent of parents today "try to spend as much time with their children as possible", they simply don't feel it's enough.
In total, 62 per cent of women with young children who work would like to give up work and be a full-time mum, while 29 per cent of dads would like to be a full-time father to their kids.
"We always hear about the chores of motherhood in the 1950s, 60s and 70s, but motherhood has never been harder than it is today," British tabloid The Sun quoted Dani Zur, General Manager of UKfamily.co.uk and mum of three, as saying.
"Most families now need a two-parent income to survive financially, which means there is less time for normal family life. It is therefore very important for parents to plan in whatever time they can with their children and also build-in some 'me time' for themselves.
"Parents today are burning out trying to fit in all the demands of modern life. But however overloaded they are it's crucial for their own health they take some time out for themselves without feeling guilty. Just 10 minutes chatting to a friend or having a long soak in the bath can revive their spirits. Parents need to be kinder to themselves.
"Dads are desperate to be more involved in their kids' lives. Society as a whole must recognise the importance of dad's role and do more to facilitate him spending quality time with his children," Zur said.
According to Life coach Suzy Greaves, the survey revealed just how many think that they could be better parents if only they had more time on their hands.
"This research shows just how many of us think we'd be a 'better parent' if we had more time. We feel guilty about everything - the amount of time we spend at work, the lack of time we have to play with our children and the amount of time our kids spend in childcare," Greaves said.
"As a result, many working parents, especially mums, are running themselves ragged trying to overcompensate.
"It's time for us to stop being self-critical and let go of our guilt - an absolutely useless emotion - and then shelve some of the tasks that take up so much of our time.
"It really doesn't matter if everything isn't crisply ironed or the toys all put away. Instead, we parents should give ourselves a pat on the back for the amazing amount we do achieve.
"Let's model happiness to our kids instead of guilt and martyrdom," she added.