Club captain Michael Devlin, Gary Gillespie and Greg Docherty all left in January after coming through the youth ranks at Accies while Louis Longridge signed for Falkirk after six years in Lanarkshire.
The quartet made more than 650 appearances between them and manager Martin Canning suffered frustration on the final day of the transfer window when he only got one of the four players he had targeted, on-loan Manchester United midfielder Charlie Scott.
Canning added four players to his first-team squad in total who had no prior experience in Scottish football but Woods is adamant they can adapt quickly with the help of their team-mates.
Speaking ahead of their Ladbrokes Premiership match at Aberdeen, Woods said: “Some of the players that have left had been part of the club for a fair few years and come through the system.
“But as harsh as it sounds, that’s football, people move on. We wish them all the best but we have to concentrate on the players that are here and moving up the table.
“It’s a very welcoming club. We just need to stick together and if there are new bodies come in, we integrate them quite quickly and go to Aberdeen and get a result.”