Allardyce is yet to lose a match since he replaced interim coach David Unsworth at the end of November.
That run has seen the Toffees climb up to ninth in the Premier League table and Bolasie believes Allardyce's organisation skills have paid dividends.
Bolasie returned to the first team on Boxing Day after a year out with cruciate knee ligament damage and is confident the club's attacking players can still flourish in their new system.
He told Sky Sports: "He's got us defending much better and he will probably come out and say now it's about the transition and how we want to play as forwards.
"We were good going forward before but not so good defending as a team. Now we're defending really well, but the transition hasn't been as good as we want it to be."