For all their progress under Mauricio Pochettino Spurs are yet to claim any silverware in the Argentine's four years in charge, leading many to suggest their emergence as one of the Premier League's powerhouses will not be complete until they do so.
However, speaking on 'The Debate' on 'Sky Sports', Strachan rejected such claims, saying that what Spurs have done already is much more impressive than winning a trophy.
"Say they win a cup. It's easy to win a cup. You can play two teams from the Championship, one from League One and one from non league, you play one from the Premier League and you win a cup. That doesn't make you a great side," he insisted.
"Being third in the Premier League is far better. If you think about the progress made over the last couple of years where they can go and play Real Madrid and stand up to them and be in the Champions League.
"If they're not successful in the Champions League, they'll be disappointed because they think they can do better, but I think they have done fantastically well.
"People say they need to balance it out with a trophy, but what is a trophy? Is the League Cup as good as what they are producing week in, week out? Everyone talks about consistency and over the last four years, they have been incredibly consistent. One team could win the FA Cup and then get relegated, so who is doing the best?
"Pochettino and his staff have done tremendously well and he is not scared to use youth either. You look at the young players that have played there and he has bought in players who have gone in there and improved which is a great thing.
"They've got to fill a big stadium, which they are doing just now, and that's great going. Here's another bit of success, as a football fan, I love watching them play football. I love watching them on the TV.
"There's a lot going on there and he might want to win a cup but I don't think it's really that important."