The home side forced the visitors to follow on during an entralling final day of the County Championship division one clash at the Ageas Bowl.
However, they were unable to snatch a much-needed victory as Lancashire edged to the close still 63 runs adrift but with seven second-innings wickets intact.
The draw left Hampshire at the foot of the top-flight table with five games remaining.
Smith, who struck a career-best 210 in his side’s first-innings total of 548 for six declared, was content his men had done everything in their power to push for glory.
The stand-in skipper, who is deputising while James Vince is on England duty, said: ‘I don’t think we could have done any more.
‘In terms of the effort and desire to win, it was all we could ask.
‘We probably didn’t create enough chances.
‘But, that said, you can’t fault the effort – we have fielded for 210 overs in a row.
‘Liam (Dawson) and Mason (Crane) bowled 100 of them and bowled particularly well.
‘We couldn’t force the win but there are a lot of positives.
‘At times the pitch appeared docile but all of a sudden it would come to life. It was a wicket which suited us.’
Hampshire travel to second-bottom Nottinghamshire for their next game, which begins on Saturday.
Smith believes there is still plenty of time for his side to escape the grip of relegation.
And he reckons Hampshire have players coming into form at a crucial time.
The former Durham batsman said: ‘Every game is important now.
‘We have to approach the next five with a winning mentality.
‘If we can come out with two wins, we can climb the table.
‘The guys are batting and bowling well and if we continue like this we are confident things will start going our way.’
Lancashire, meanwhile, are one of a number of sides who could still get dragged into the relegation scrap.
And Ashley Giles knows how vital it was to avoid defeat.
Lancashire’s director of cricket said: ‘The draw was the most important thing, particularly against Hampshire.
‘We wanted to win the game but we were on the wrong end of the toss.
‘The conditions yesterday were a bit more challenging. The ball had started to spin and bite.
‘All our focus was getting over the follow on. We didn’t but we were fine.’
Giles saved extra praise for 19-year-old Haseeb Hameed – who complied his second half-century of the game as he steered Lancashire to the draw.
He said: ‘Sometimes you talk about a player and their age but some guys just get it and Has is one of those.
‘He has a huge amount of maturity and loves his batting. He’s going to have a bright future.’