Victory at the Arena took the club up to fifth spot and ensure qualification.
The coach said he was happy with the early drive and congratulated winger Brandon Whistle on his first goal of the season - and the first of his professional career.
Steelers had taken a 4-0 lead in the first session, adding another in the second.
Barrasso said there had been no risk involved in the unexpected performance of Ben O'Connor, who is recovering from a left ankle injury.
He added the travel plans for the Belfast Giants' game, today Sunday, were not perfect.
It is the penultimate league outing of the regular season.
Hear what he has to say on our video.
Saturday 23rd March
Cardiff Devils 4 Manchester Storm 0
Fife Flyers 3 Guildford Flames 2 (PS)
Glasgow Clan 0 Nottingham Panthers 4
Sheffield Steelers 5 Milton Keynes Lightning 1
Sunday 24th March
Belfast Giants v Sheffield Steelers - 4.00pm
Dundee Stars v Cardiff Devils - 5.00pm
Fife Flyers v Nottingham Panthers - 6.30pm
Guildford Flames v Coventry Blaze - 6.00pm