Giving evidence to Westminster’s Scottish Affairs Committee on the relationship between the UK and Scottish Governments, Lord Wallace said the daydreaming occurred during Joint Ministerial Committees (JMCs).
The Liberal Democrat peer, who was Scotland’s deputy first minister from Scottish devolution until 2005, with short spells as interim first minister, questioned the formal inter-governmental machinery at the time.
JMC meetings involve devolved government leaders along with those of the UK Government.
Lord Wallace said: “The Joint Ministerial Committee as it were at the top level of Prime Minister, Deputy Prime Minister, First Minister, Deputy First Minister.
“I remember meeting in Edinburgh, in Cardiff and by the time it came to the third meeting in Downing Street, I don’t think I’m exaggerating to say that Tony Blair spent most of the time looking out the window.
“But actually, nothing much was achieved at them.
“You were failing to understand the point of them and that’s when they fell away and I think they were only revived after the Scottish National Party came to office in Edinburgh - where there’s perhaps arguably a greater need for them.”