Los Verdiblancos also conceded eight goals in those two fixtures but were hampered by having players sent off in both games and Mel is hoping to get back on track at home to Real Sociedad this weekend.
He told the club's website: "We have had difficulties in keeping a clean sheet after two games in which we did so. They were not normal games but it is also certain that we need to look at our errors and don't hide ourselves from them.
"We have to improve in many things and no team is at 100% or doesn't have things to aspire to. We are not an exception and the team has changed a lot in respect to last year.
"The problem is we weren't given time to savour the victory over Espanyol.
"The start to the league has been good. If we win, 12 points will put us in the top seven or eight. I don't see any sort of drama or hurry. We have to keep working in the same way."
Betis will be boosted by the return of Paulao to the heart of the defence after he missed the last two games, while Ruben Castro will return up front after being rested from the start against Malaga.
Real Sociedad manager Philippe Montanier, meanwhile, is looking to curtail his side's awful run of form on the road.
Victory over Athletic Bilbao in the Basque derby last weekend extended their 100% record at home, but the Txuri-urdin haven't won away in the league since January and have lost on all three of their trips so far this season.
Montanier told Diario Vasco: "The victory in the derby gave us confidence and ambition to win in Seville.
"In the league it is difficult to pick up points away, but the evolution of the team is positive. We are concentrated and we know that to have a good season we need to take points away from home."
Imanol Agirretxe is a doubt for the visitors so Carlos Vela should return up front after scoring his second goal of the campaign as a substitute against Athletic last time out.