The Lions drew 2-2 with Cowdenbeath on Tuesday after losing a last-minute equaliser and were missing Stefan Scougall, Tony Andreu, Marc McNulty and Keaghan Jacobs – but the West Lothian are still just a point behind Falkirk in that third spot.
As they take on Hamilton Academical tomorrow, Burchill said the senior players can help the younger members of the team to see out matches.
He said: “We’ve got a lot of guys missing who are big players for us but you’ve got to be able to cope with that sometimes. I think we had a team out there on Tuesday who were capable of winning the game.
“Cowdenbeath made it difficult for us but we showed a lot of fight to get in front. To lose a goal at the end was very disappointing and it was two points thrown away again.
“We need to be a bit more clever than that and in those situations know how to see out the game.
“Mentally we have to be a bit tougher. We know it’s a young team but we have lots of senior guys who should be able to drag us through.”
Tomorrow’s game sees the Lions finally roll out their special offer of just £5 entry for all supporters, a deal initially offered back in December, but three times thwarted thanks to the weather.
Club director David Stoker said: “We’ve been really unlucky with the weather . The reason we selected the game initially was the timing of it. Money’s traditionally tight for people with Christmas, so we wanted to do something to help that.
“Of course, at that time of year a call off is always possible but when you get to the middle of March it’s a bit more of a surprise that it’s still happening. That’s just the Scottish weather I guess.
“What will be interesting to see is the take up of the £5 offer, because if we do take in more money than a usual game it will give us on the board something to really think about.”