Burrow guided the Swans to within 180 minutes of Wembley in 1993 - a run of 5 wins in the last 6 league matches secured a playoff place, and with five minutes remaining of the first leg of the semi-final against West Brom, the Swans were 2-0 up and looking comfortable. Andy McFarlance netted in an unfortunate own goal when the ball rebounded off the crossbar then into the net off his knee to give West Brom a lifeline, and two early goals followed by the sending off of Colin West in the away leg made it almost impossible for the Swans to make a fightback.

Although the league season the following year failed to live up the previous one, mainly due to the offloading of certain players, Burrows guided the Swans to Wembley for the first occasion in their history for the final of the Autoglass Trophy. Wins over Plymouth & Exeter in the group stage followed by triumphs over Exeter again, Port Vale, Leyton Orient and Wycombe over two legs saw the Swans play Huddersfield in a final that ended 1-1. Chairman Doug Sharpe brought back the memorable hat, and the Swans went on to victory 2-0 on penalties.