Liverpool offloaded 20-year-old striker Brewster to Premier League rivals Sheffield United earlier in the month for a fee of £23.5million.
Anfield legend Thompson wanted Brewster to remain at Liverpool, however, and says his former club should instead have sold Divock Origi and Xherdan Shaqiri.
‘On the outgoings [at Liverpool], I’m disappointed that they decided to let Rhian Brewster go,’ Thompson told Paddy Power.
‘I’d like him to have stayed. I can see some of the reasons why, but if you were asking me whether to go with Brewster or Divock Origi, for me, it’d be Origi going.
‘But on the football side, I can see he isn’t playing as many games, so maybe it’ll get him that first team experience.
‘There’s not too many forwards that have the aggression that Brewster has though.
‘There’s a couple of others that could have gone, Xherdan Shaqiri for example could’ve brought a few quid in.
‘Maybe the outgoings haven’t gone the way they’d like – but the incomings have been really good.’
Diogo Jota, Thiago Alcantara and Kostas Tsimikas joined Klopp’s squad during the summer transfer window and Thompson believes all three players will make an impact as Liverpool look to defend the Premier League title.
He added: ‘Liverpool had a really decent transfer market. I heard people saying following the defeat that they felt they hadn’t had a good window – but that, to me, is harsh.
‘We needed a little bit of creativity, and it had been long talked about, and low and behold we ended up with Thiago. You couldn’t have ticked a box much better.
‘He can keep the ball when you want him to but can pass it quickly also. Great signing!
‘We were looking at someone else in a more attacking position, and I did a lot of Wolves games last year, and I was absolutely raving about Diogo Jota for months!
‘This fella could play for all of the big clubs – no disrespect to Wolves – and when Liverpool signed him I thought it was a bit like the Sadio Mane signing.
‘When he joined, people were saying: ‘Sadio Mane? Eh, plays for Southampton, is he any good?’ and look at him now, a superstar. A world class player.
‘And I think Diogo Jota can bring that to the club once again. He’s a terrific signing.
‘If I was grading their performance in the transfer market, I’d rate it a solid 8/10 in terms of the incoming signings.’