Jan Bednarek says Southampton will not ease off as they look to equal a club record unbeaten run set in 1921-22.
Saints are on an 18-match unbeaten run in the Championship, going back to 23 September, but remain three points off the automatic promotion places.
Saturday's FA Cup third-round win means they can now match their record 20 games unbeaten across all competitions.
Bednarek told BBC Radio Solent : "It's not bad but we are not where we want to be - it's not enough."
Southampton need to avoid defeat at home to Sheffield Wednesday to move level with those club records.