Burnley — who signed Dean Marney, Chris Iwelumo and Ross Wallace ahead of their Championship return that summer — were billed as one of the favourites for promotion.
However, they failed to match their expectations as they finished eighth in the division, seven points off the play-offs, after picking up a solitary point from a possible 18 in a spell from mid-March.
"It's a bit different now for Burnley because they'd established themselves in the Premier League," said the former Scotland international. "When we got promoted the club hadn't been in the top level since the '70s and they'd never played in the Premier League so we did it against all odds.
"We were expected to come back down straight away, we gave it a good shot and were good in the first half of the season, but the quality overtook us in the second part.
"I felt when we came back down to the Championship the expectancy was too high to go straight back up. We all had the ambition to do that in our first season, but there were still 6-10 clubs in the Championship that were bigger than us."
Alexander's final season at Turf Moor was the penultimate campaign of his career. The former Preston North End favourite played 36 times in 2010-11, scoring four times, which took his overall tally to 178 appearances and 24 goals in all competitions.
The ex-Fleetwood Town, Scunthorpe United and Salford City manager feels the expectation will be on Burnley to go straight back up following six successive seasons in the top flight.
They're currently priced around 4/1 with most bookmakers to be successful in Vincent Kompany's first season in charge, behind the likes of Norwich City, Watford, Middlesbrough, Sheffield United and West Bromwich Albion.
Alexander said: "It's an incredibly difficult league to compete in, you've seen giants like Newcastle United and Leeds United coming down in the past and finding it difficult.
"Burnley is a different club now to what it was in 2010 when we came down, it's had a long time in the Premier League, the training facilities are frightening compared to what we had, so the expectation will be there, and probably rightly so.
"It's all about winning games on the pitch, though, and you have to put that pressure and expectation to the side, you have to keep it under control. Whatever you want to achieve in football, ultimately, you can only do it if you win games, that's what the biggest focus has to be on."
After the Clarets lost their PL status on the final day of term, with Leeds United profiting, Alexander concluded: "You've got to stop yourself thinking about the past, don't look at the fixtures you could've been involved in, it's a very dangerous thing to do. You've got to focus on what's directly in front of you, rather than what's behind you.
"Feeling sorry for yourself or looking back on what could have been is a waste of time and takes your focus away. Embrace it and look forward to it."